Longitudinal profiles of bounded outcome scores as predictors for disease activity in rheumatoid arthritis patients: a joint modeling approach

A variety of statistical approaches have been suggested in the literature for the analysis of bounded outcome scores (BOS). In this paper, we suggest a statistical approach when BOSs are repeatedly measured over time and used as predictors in a regression model. Instead of directly using the BOS as a predictor, we propose to extend the approaches suggested in [16 E. Lesaffre, D. Rizopoulos, and R. Tsonaka, The logistics-transform for bounded outcome scores, Biostatistics 8 (2007), pp. 72–85. doi: 10.1093/biostatistics/kxj034[Crossref], [PubMed], [Web of Science ®] , [Google Scholar],21 M. Molas and E. Lesaffre, A comparison of the three random effects approaches to analyse repeated bounded outcome scores with an application in a stroke revalidation study, Stat. Med. 27 (2008), pp. 6612–6633. doi: 10.1002/sim.3432[Crossref], [PubMed], [Web of Science ®] , [Google Scholar],28 R. Tsonaka, D. Rizopoulos, and E. Lesaffre, Power and sample size calculations for discrete bounded outcome scores, Stat. Med. 25 (2006), pp. 4241–4252. doi: 10.1002/sim.2679[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] to a joint modeling setting. Our approach is illustrated on longitudinal profiles of multiple patients’ reported outcomes to predict the current clinical status of rheumatoid arthritis patients by a disease activities score of 28 joints (DAS28). Both a maximum likelihood as well as a Bayesian approach is developed.     

Testing for sphericity in a two-way error components panel data model

This article is concerned with sphericity test for the two-way error components panel data model. It is found that the John statistic and the bias-corrected LM statistic recently developed by Baltagi et al. (2011 Baltagi, B. H., Feng, Q., Kao, C. (2011). Testing for sphericity in a fixed effects panel data model. Econometrics Journal 14:25–47.[Crossref], [Web of Science ®] , [Google Scholar])Baltagi et al. (2012 Baltagi, B. H., Feng, Q., Kao, C. (2012). A Lagrange multiplier test for cross-sectional dependence in a fixed effects panel data model. Journal of Econometrics 170:164–177.[Crossref], [Web of Science ®] , [Google Scholar], which are based on the within residuals, are not helpful under the present circumstances even though they are in the one-way fixed effects model. However, we prove that when the within residuals are properly transformed, the resulting residuals can serve to construct useful statistics that are similar to those of Baltagi et al. (2011 Baltagi, B. H., Feng, Q., Kao, C. (2011). Testing for sphericity in a fixed effects panel data model. Econometrics Journal 14:25–47.[Crossref], [Web of Science ®] , [Google Scholar])Baltagi et al. (2012 Baltagi, B. H., Feng, Q., Kao, C. (2012). A Lagrange multiplier test for cross-sectional dependence in a fixed effects panel data model. Journal of Econometrics 170:164–177.[Crossref], [Web of Science ®] , [Google Scholar]). Simulation results show that the newly proposed statistics perform well under the null hypothesis and several typical alternatives.     

A Bayesian approach to analyse overdispersed longitudinal count data

In this paper, we consider a model for repeated count data, with within-subject correlation and/or overdispersion. It extends both the generalized linear mixed model and the negative-binomial model. This model, proposed in a likelihood context [17 G. Molenberghs, G. Verbeke, and C.G.B. Demétrio, An extended random-effects approach to modeling repeated, overdispersion count data, Lifetime Data Anal. 13 (2007), pp. 457–511.[Web of Science ®] , [Google Scholar],18 G. Molenberghs, G. Verbeke, C.G.B. Demétrio, and A. Vieira, A family of generalized linear models for repeated measures with normal and conjugate random effects, Statist. Sci. 25 (2010), pp. 325–347. doi: 10.1214/10-STS328[Crossref], [Web of Science ®] , [Google Scholar]] is placed in a Bayesian inferential framework. An important contribution takes the form of Bayesian model assessment based on pivotal quantities, rather than the often less adequate DIC. By means of a real biological data set, we also discuss some Bayesian model selection aspects, using a pivotal quantity proposed by Johnson [12 V.E. Johnson, Bayesian model assessment using pivotal quantities, Bayesian Anal. 2 (2007), pp. 719–734. doi: 10.1214/07-BA229[Crossref], [Web of Science ®] , [Google Scholar]].     

Random Effects,Fixed Effects and Hausman's Test for the Generalized Mixed Regressive Spatial Autoregressive Panel Data Model

This article suggests random and fixed effects spatial two-stage least squares estimators for the generalized mixed regressive spatial autoregressive panel data model. This extends the generalized spatial panel model of Baltagi et al. (2013 Baltagi, B. H., Egger, P., Pfaffermayr, M. (2013). A generalized spatial panel data model with random effects. Econometric Reviews 32:650–685.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) by the inclusion of a spatial lag term. The estimation method utilizes the Generalized Moments method suggested by Kapoor et al. (2007 Kapoor, M., Kelejian, H. H., Prucha, I. R. (2007). Panel data models with spatially correlated error components. Journal of Econometrics 127(1):97–130.[Crossref], [Web of Science ®] , [Google Scholar]) for a spatial autoregressive panel data model. We derive the asymptotic distributions of these estimators and suggest a Hausman test a la Mutl and Pfaffermayr (2011 Mutl, J., Pfaffermayr, M. (2011). The Hausman test in a Cliff and Ord panel model. Econometrics Journal 14:48–76.[Crossref], [Web of Science ®] , [Google Scholar]) based on the difference between these estimators. Monte Carlo experiments are performed to investigate the performance of these estimators as well as the corresponding Hausman test.     

A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models

This article considers constructing confidence intervals for the date of a structural break in linear regression models. Using extensive simulations, we compare the performance of various procedures in terms of exact coverage rates and lengths of the confidence intervals. These include the procedures of Bai (1997 Bai, J. (1997). Estimation of a change point in multiple regressions. Review of Economics and Statistics 79:551–563.[Crossref], [Web of Science ®] , [Google Scholar]) based on the asymptotic distribution under a shrinking shift framework, Elliott and Müller (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.[Crossref], [Web of Science ®] , [Google Scholar]) based on inverting a test locally invariant to the magnitude of break, Eo and Morley (2015 Eo, Y., Morley, J. (2015). Likelihood-ratio-based confidence sets for the timing of structural breaks. Quantitative Economics 6:463–497.[Crossref], [Web of Science ®] , [Google Scholar]) based on inverting a likelihood ratio test, and various bootstrap procedures. On the basis of achieving an exact coverage rate that is closest to the nominal level, Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.[Crossref], [Web of Science ®] , [Google Scholar]) approach is by far the best one. However, this comes with a very high cost in terms of the length of the confidence intervals. When the errors are serially correlated and dealing with a change in intercept or a change in the coefficient of a stationary regressor with a high signal-to-noise ratio, the length of the confidence interval increases and approaches the whole sample as the magnitude of the change increases. The same problem occurs in models with a lagged dependent variable, a common case in practice. This drawback is not present for the other methods, which have similar properties. Theoretical results are provided to explain the drawbacks of Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.[Crossref], [Web of Science ®] , [Google Scholar]) method.     

Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach

The density power divergence (DPD) measure, defined in terms of a single parameter α, has proved to be a popular tool in the area of robust estimation [1 A. Basu, I.R. Harris, N.L. Hjort and M.C. Jones, Robust and efficient estimation by minimizing a density power divergence, Biometrika 85 (1998), pp. 549–559. doi: 10.1093/biomet/85.3.549[Crossref], [Web of Science ®] , [Google Scholar]]. Recently, Ghosh and Basu [5 A. Ghosh and A. Basu, Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression, Electron. J. Stat. 7 (2013), pp. 2420–2456. doi: 10.1214/13-EJS847[Crossref], [Web of Science ®] , [Google Scholar]] rigorously established the asymptotic properties of the MDPDEs in case of independent non-homogeneous observations. In this paper, we present an extensive numerical study to describe the performance of the method in the case of linear regression, the most common setup under the case of non-homogeneous data. In addition, we extend the existing methods for the selection of the optimal robustness tuning parameter from the case of independent and identically distributed (i.i.d.) data to the case of non-homogeneous observations. Proper selection of the tuning parameter is critical to the appropriateness of the resulting analysis. The selection of the optimal robustness tuning parameter is explored in the context of the linear regression problem with an extensive numerical study involving real and simulated data.     

Analysis of discrete lifetime data under middle-censoring and in the presence of covariates

‘Middle censoring’ is a very general censoring scheme where the actual value of an observation in the data becomes unobservable if it falls inside a random interval (L, R) and includes both left and right censoring. In this paper, we consider discrete lifetime data that follow a geometric distribution that is subject to middle censoring. Two major innovations in this paper, compared to the earlier work of Davarzani and Parsian [3 N. Davarzani and A. Parsian, Statistical inference for discrete middle-censored data, J. Statist. Plan. Inference 141 (2011), pp. 1455–1462. doi: 10.1016/j.jspi.2010.10.012[Crossref], [Web of Science ®] , [Google Scholar]], include (i) an extension and generalization to the case where covariates are present along with the data and (ii) an alternate approach and proofs which exploit the simple relationship between the geometric and the exponential distributions, so that the theory is more in line with the work of Iyer et al. [6 S.K. Iyer, S.R. Jammalamadaka, and D. Kundu, Analysis of middle censored data with exponential lifetime distributions, J. Statist. Plan. Inference 138 (2008), pp. 3550–3560. doi: 10.1016/j.jspi.2007.03.062[Crossref], [Web of Science ®] , [Google Scholar]]. It is also demonstrated that this kind of discretization of life times gives results that are close to the original data involving exponential life times. Maximum likelihood estimation of the parameters is studied for this middle-censoring scheme with covariates and their large sample distributions discussed. Simulation results indicate how well the proposed estimation methods work and an illustrative example using time-to-pregnancy data from Baird and Wilcox [1 D.D. Baird and A.J. Wilcox, Cigarette smoking associated with delayed conception, J, Am. Med. Assoc. 253 (1985), pp. 2979–2983. doi: 10.1001/jama.1985.03350440057031[Crossref], [Web of Science ®] , [Google Scholar]] is included.     

Hip fracture prediction from a new classification algorithm based on recursive partitioning methods

Classification and regression tree has been useful in medical research to construct algorithms for disease diagnosis or prognostic prediction. Jin et al. 7 Jin, H., Lu, Y., Harris, R. T., Black, D., Stone, K., Hochberg, M. and Genant, H. 2004. Classification algorithms for hip fracture prediction base on recursive partitioning methods. Med. Decis. Mak., 24: 386–398. (doi:10.1177/0272989X04267009)[Crossref], [PubMed], [Web of Science ®] , [Google Scholar] developed a robust and cost-saving tree (RACT) algorithm with application in classification of hip fracture risk after 5-year follow-up based on the data from the Study of Osteoporotic Fractures (SOF). Although conventional recursive partitioning algorithms have been well developed, they still have some limitations. Binary splits may generate a big tree with many layers, but trinary splits may produce too many nodes. In this paper, we propose a classification approach combining trinary splits and binary splits to generate a trinary–binary tree. A new non-inferiority test of entropy is used to select the binary or trinary splits. We apply the modified method in SOF to construct a trinary–binary classification rule for predicting risk of osteoporotic hip fracture. Our new classification tree has good statistical utility: it is statistically non-inferior to the optimum binary tree and the RACT based on the testing sample and is also cost-saving. It may be useful in clinical applications: femoral neck bone mineral density, age, height loss and weight gain since age 25 can identify subjects with elevated 5-year hip fracture risk without loss of statistical efficiency.     

An intuitive clustering algorithm for spherical data with application to extrasolar planets

This paper proposes an intuitive clustering algorithm capable of automatically self-organizing data groups based on the original data structure. Comparisons between the propopsed algorithm and EM [1 A. Banerjee, I.S. Dhillon, J. Ghosh, and S. Sra, Clustering on the unit hypersphere using von Mises–Fisher distribution, J. Mach. Learn. Res. 6 (2005), pp. 1–39. [Google Scholar]] and spherical k-means [7 I.S. Dhillon and D.S. Modha, Concept decompositions for large sparse text data using clustering, Mach. Learn. 42 (2001), pp. 143–175. doi: 10.1023/A:1007612920971[Crossref], [Web of Science ®] , [Google Scholar]] algorithms are given. These numerical results show the effectiveness of the proposed algorithm, using the correct classification rate and the adjusted Rand index as evaluation criteria [5 J.-M. Chiou and P.-L. Li, Functional clustering and identifying substructures of longitudinal data, J. R. Statist. Soc. Ser. B. 69 (2007), pp. 679–699. doi: 10.1111/j.1467-9868.2007.00605.x[Crossref] , [Google Scholar],6 J.-M. Chiou and P.-L. Li, Correlation-based functional clustering via subspace projection, J. Am. Statist. Assoc. 103 (2008), pp. 1684–1692. doi: 10.1198/016214508000000814[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. In 1995, Mayor and Queloz announced the detection of the first extrasolar planet (exoplanet) around a Sun-like star. Since then, observational efforts of astronomers have led to the detection of more than 1000 exoplanets. These discoveries may provide important information for understanding the formation and evolution of planetary systems. The proposed clustering algorithm is therefore used to study the data gathered on exoplanets. Two main implications are also suggested: (1) there are three major clusters, which correspond to the exoplanets in the regimes of disc, ongoing tidal and tidal interactions, respectively, and (2) the stellar metallicity does not play a key role in exoplanet migration.     

MSE Performance of a Heterogeneous Pre-Test Ridge Regression Estimator

This article describes how diagnostic procedures were derived for symmetrical nonlinear regression models, continuing the work carried out by Cysneiros and Vanegas (2008 Cysneiros , F. J. A. , Vanegas , L. H. ( 2008 ). Residuals and their statistical properties in symmetrical nonlinear models . Statist. Probab. Lett. 78 : 3269 – 3273 .[Crossref], [Web of Science ®] , [Google Scholar]) and Vanegas and Cysneiros (2010 Vanegas , L. H. , Cysneiros , F. J. A. ( 2010 ). Assesment of diagnostic procedures in symmetrical nonlinear regression models . Computat. Statist. Data Anal. 54 : 1002 – 1016 .[Crossref], [Web of Science ®] , [Google Scholar]), who showed that the parameters estimates in nonlinear models are more robust with heavy-tailed than with normal errors. In this article, we focus on assessing if the robustness of this kind of models is also observed in the inference process (i.e., partial F-test). Symmetrical nonlinear regression models includes all symmetric continuous distributions for errors covering both light- and heavy-tailed distributions such as Student-t, logistic-I and -II, power exponential, generalized Student-t, generalized logistic, and contaminated normal. Firstly, a statistical test is shown to evaluating the assumption that the error terms all have equal variance. The results of simulation studies which describe the behavior of the test for heteroscedasticity proposed in the presence of outliers are then given. To assess the robustness of inference process, we present the results of a simulation study which described the behavior of partial F-test in the presence of outliers. Also, some diagnostic procedures are derived to identify influential observations on the partial F-test. As ilustration, a dataset described in Venables and Ripley (2002 Venables , W. N. , Ripley , B. D. ( 2002 ). Modern Applied with S. , 4th ed. New York : Springer .[Crossref] , [Google Scholar]), is also analyzed.     

Some Fundamental Properties of a Multivariate von Mises Distribution

In application areas like bioinformatics, multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modeling of such situations is to use mixtures of unimodal distributions. In the literature (Mardia et al., 2012 Mardia , K. V. , Kent , J. T. , Zhang , Z. , Taylor , C. , Hamelryck , T. ( 2012 ). Mixtures of concentrated multivariate sine distributions with applications to bioinformatics . J. Appl. Stat. 39 : 2475 – 2492 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), the multivariate von Mises distribution, also known as the multivariate sine distribution, has been suggested for components of such models, but work in the area has been hampered by the fact that no good criteria for the von Mises distribution to be unimodal were available. In this article we study the question about when a multivariate von Mises distribution is unimodal. We give sufficient criteria for this to be the case and show examples of distributions with multiple modes when these criteria are violated. In addition, we propose a method to generate samples from the von Mises distribution in the case of high concentration.     

Is Each NPMLE of a Continuous Bivariate Distribution Function with Singly Right-Censored Data Really Inconsistent?

We consider non-parametric estimation of a continuous cdf of a random vector (X ₁, X ₂). With bivariate RC data, it is stated in van der Laan (1996 Van der Laan , M. J. ( 1996 ) Efficient estimation in the bivariate censoring model and repairing NPMLE . Ann. Statist. 24 : 596 – 627 .[Crossref], [Web of Science ®] , [Google Scholar], p. 598¹⁰, Ann. Statist.), Quale et al. (2006 Quale , C. M. , van der Laan , M. J. , Robins , J. R. ( 2006 ). Locally efficient estimation with bivariate right-censored data . JASA. 101 : 1076 – 1084 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], JASA) etc. that “it is well known that the NPMLE for continuous data is inconsistent (Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar])).” The claim is based on a result in Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], p.1352, Ann. Statist.) that if X ₁ is right censored but not X ₂, then common ways for defining one NPMLE lead to inconsistency. If X ₁ is right censored and X ₂ is type I right-censored (which includes the case in Tsai et al.), we present a consistent NPMLE. The result corrects a common misinterpretation of Tsai's example (Tsai et al., 1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], Ann. Statist.).     

Improving the Power of Tests of Stochastic Dominance

We extend Hansen's (2005) recentering method to a continuum of inequality constraints to construct new Kolmogorov–Smirnov tests for stochastic dominance of any pre-specified order. We show that our tests have correct size asymptotically, are consistent against fixed alternatives and are unbiased against some N^?1/2 local alternatives. It is shown that by avoiding the use of the least favorable configuration, our tests are less conservative and more powerful than Barrett and Donald's (2003) and in some simulation examples we consider, we find that our tests can be more powerful than the subsampling test of Linton et al. (2005 Linton, O., Maasoumi, E., Whang, Y.-J. (2005). Consistent testing for stochastic dominance under general sampling schemes. The Review of Economic Studies 72:735–765.[Crossref], [Web of Science ®] , [Google Scholar]). We apply our method to test stochastic dominance relations between Canadian income distributions in 1978 and 1986 as considered in Barrett and Donald (2003 Barrett, G. F., Donald, S. G. (2003). Consistent tests for stochastic dominance. Econometrica 71: 71–104.[Crossref], [Web of Science ®] , [Google Scholar]) and find that some of the hypothesis testing results are different using the new method.     

First difference transformation in panel VAR models: Robustness,estimation, and inference

This article considers estimation of Panel Vector Autoregressive Models of order 1 (PVAR(1)) with focus on fixed T consistent estimation methods in First Differences (FD) with additional strictly exogenous regressors. Additional results for the Panel FD ordinary least squares (OLS) estimator and the FDLS type estimator of Han and Phillips (2010 Han, C., Phillips, P. C. B. (2010). Gmm estimation for dynamic panels with fixed effects and strong instruments at unity. Econometric Theory 26:119–151.[Crossref], [Web of Science ®] , [Google Scholar]) are provided. Furthermore, we simplify the analysis of Binder et al. (2005 Binder, M., Hsiao, C., Pesaran, M. H. (2005). Estimation and inference in short panel vector autoregressions with unit root and cointegration. Econometric Theory 21:795–837.[Crossref], [Web of Science ®] , [Google Scholar]) by providing additional analytical results and extend the original model by taking into account possible cross-sectional heteroscedasticity and presence of strictly exogenous regressors. We show that in the three wave panel the log-likelihood function of the unrestricted Transformed Maximum Likelihood (TML) estimator might violate the global identification assumption. The finite-sample performance of the analyzed methods is investigated in a Monte Carlo study.     

Empirical Likelihood in Causal Inference

This paper discusses the estimation of average treatment effects in observational causal inferences. By employing a working propensity score and two working regression models for treatment and control groups, Robins et al. (1994 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1994 ). Estimation of regression coefficients when some regressors are not always observed . Journal of the American Statistical Association 89 : 846 – 866 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 1995 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1995 ). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data . Journal of the American Statistical Association 90 : 106 – 121 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) introduced the augmented inverse probability weighting (AIPW) method for estimation of average treatment effects, which extends the inverse probability weighting (IPW) method of Horvitz and Thompson (1952 Horvitz , D. G. , Thompson , D. J. ( 1952 ). A generalization of sampling without replacement from a finite universe . Journal of the American Statistical Association 47 : 663 – 685 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]); the AIPW estimators are locally efficient and doubly robust. In this paper, we study a hybrid of the empirical likelihood method and the method of moments by employing three estimating functions, which can generate estimators for average treatment effects that are locally efficient and doubly robust. The proposed estimators of average treatment effects are efficient for the given choice of three estimating functions when the working propensity score is correctly specified, and thus are more efficient than the AIPW estimators. In addition, we consider a regression method for estimation of the average treatment effects when working regression models for both the treatment and control groups are correctly specified; the asymptotic variance of the resulting estimator is no greater than the semiparametric variance bound characterized by the theory of Robins et al. (1994 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1994 ). Estimation of regression coefficients when some regressors are not always observed . Journal of the American Statistical Association 89 : 846 – 866 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 1995 Robins , J. M. , Rotnitzky , A. , Zhao , L. P. ( 1995 ). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data . Journal of the American Statistical Association 90 : 106 – 121 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Finally, we present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification.     

Likelihood-based panel cointegration test in the presence of a linear time trend and cross-sectional dependence

This article proposes a new likelihood-based panel cointegration rank test which extends the test of Örsal and Droge (2014 Örsal, D. D. K., Droge, B. (2014). Panel cointegration testing in the presence of a time trend. Computational Statistics and Data Analysis 76:377–390.[Crossref], [Web of Science ®] , [Google Scholar]) (henceforth panel SL test) to dependent panels. The dependence is modelled by unobserved common factors which affect the variables in each cross-section through heterogeneous loadings. The data are defactored following the panel analysis of nonstationarity in idiosyncratic and common components (PANIC) approach of Bai and Ng (2004 Bai, J., Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica 72(4):1127–1177.[Crossref], [Web of Science ®] , [Google Scholar]) and the cointegrating rank of the defactored data is then tested by the panel SL test. A Monte Carlo study demonstrates that the proposed testing procedure has reasonable size and power properties in finite samples.     

A Comparison of Procedures for Controlling the False Discovery Rate in the Presence of Small Variance Genes: A Simulation Study

The Significance Analysis of Microarrays (SAM; Tusher et al., 2001 Tusher , V. G. , Tibshirani , R. , Chu , G. ( 2001 ). Significance analysis of microarrys applied to the ionizing radiation response . Proceedings of the National Academy of Sciences 98 : 5116 – 5121 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) method is widely used in analyzing gene expression data while controlling the FDR by using resampling-based procedure in the microarray setting. One of the main components of the SAM procedure is the adjustment of the test statistic. The introduction of the fudge factor to the test statistic aims at deflating the large value of test statistics due to the small standard error of gene-expression. Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) pointed out that the fudge factor does not effectively improve the power and the control of the FDR as compared to the SAM procedure without the fudge factor in the presence of small variance genes. Motivated by the simulation results presented in Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), in this article, we extend our study to compare several methods for choosing the fudge factor in the modified t-type test statistics and use simulation studies to investigate the power and the control of the FDR of the considered methods.     

Flexible parametric modelling of the hazard function in breast cancer studies

In cancer research, study of the hazard function provides useful insights into disease dynamics, as it describes the way in which the (conditional) probability of death changes with time. The widely utilized Cox proportional hazard model uses a stepwise nonparametric estimator for the baseline hazard function, and therefore has a limited utility. The use of parametric models and/or other approaches that enables direct estimation of the hazard function is often invoked. A recent work by Cox et al. [6 Cox, C., Chu, H., Schneider, M. F. and Munoz, A. 2007. Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Stat. Med., 26: 4352–4374. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] has stimulated the use of the flexible parametric model based on the Generalized Gamma (GG) distribution, supported by the development of optimization software. The GG distribution allows estimation of different hazard shapes in a single framework. We use the GG model to investigate the shape of the hazard function in early breast cancer patients. The flexible approach based on a piecewise exponential model and the nonparametric additive hazards model are also considered.     

Evaluating the relative merits of competing models based on empirical likelihood ratio test

Competing models arise naturally in many research fields, such as survival analysis and economics, when the same phenomenon of interest is explained by different researcher using different theories or according to different experiences. The model selection problem is therefore remarkably important because of its great importance to the subsequent inference; Inference under a misspecified or inappropriate model will be risky. Existing model selection tests such as Vuong's tests [26 Q.H. Vuong, Likelihood ratio test for model selection and non-nested hypothesis, Econometrica 57 (1989), pp. 307–333. doi: 10.2307/1912557[Crossref], [Web of Science ®] , [Google Scholar]] and Shi's non-degenerate tests [21 X. Shi, A non-degenerate Vuong test, Quant. Econ. 6 (2015), pp. 85–121. doi: 10.3982/QE382[Crossref], [Web of Science ®] , [Google Scholar]] suffer from the variance estimation and the departure of the normality of the likelihood ratios. To circumvent these dilemmas, we propose in this paper an empirical likelihood ratio (ELR) tests for model selection. Following Shi [21 X. Shi, A non-degenerate Vuong test, Quant. Econ. 6 (2015), pp. 85–121. doi: 10.3982/QE382[Crossref], [Web of Science ®] , [Google Scholar]], a bias correction method is proposed for the ELR tests to enhance its performance. A simulation study and a real-data analysis are provided to illustrate the performance of the proposed ELR tests.     

Forward Moving Average Representations for MA Processes of Finite Order: Multivariate Stationary and Periodically Correlated

Soltani and Mohammadpour (2006 Soltani , A. R. , Mohammadpour , M. (2006). Moving average representations for multivariate stationary processes. J. Time Ser. Anal. 27(6):831–841.[Crossref], [Web of Science ®] , [Google Scholar]) observed that in general the backward and forward moving average coefficients, correspondingly, for the multivariate stationary processes, unlike the univariate processes, are different. This has stimulated researches concerning derivations of forward moving average coefficients in terms of the backward moving average coefficients. In this article we develop a practical procedure whenever the underlying process is a multivariate moving average (or univariate periodically correlated) process of finite order. Our procedure is based on two key observations: order reduction (Li, 2005 Li , L. M. ( 2005 ). Factorization of moving average spectral densities by state space representations and stacking . J. Multivariate Anal. 96 : 425 – 438 .[Crossref], [Web of Science ®] , [Google Scholar]) and first-order analysis (Mohammadpour and Soltani, 2010 Mohammadpour , M. , Soltani , A. R. ( 2010 ). Forward moving average representation for multivariate MA(1) processes . Commun. Statist. Theory Meth. 39 : 729 – 737 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]).