Weighted simulated integrated conditional moment tests for parametric conditional distributions of stationary time series processes

In this article, we propose a weighted simulated integrated conditional moment (WSICM) test of the validity of parametric specifications of conditional distribution models for stationary time series data, by combining the weighted integrated conditional moment (ICM) test of Bierens (1984 Bierens, H. J. (1984). Model specification testing of time series regressions. Journal of Econometrics 26:323–353.[Crossref], [Web of Science ®] , [Google Scholar]) for time series regression models with the simulated ICM test of Bierens and Wang (2012 Bierens, H. J., Wang, L. (2012). Integrated conditional moment tests for parametric conditional distributions. Econometric Theory 28:328–362.[Crossref], [Web of Science ®] , [Google Scholar]) of conditional distribution models for cross-section data. To the best of our knowledge, no other consistent test for parametric conditional time series distributions has been proposed yet in the literature, despite consistency claims made by some authors.     

Weighting variables in Kohonen competitive learning algorithms

This paper presents a new variable weight method, called the singular value decomposition (SVD) approach, for Kohonen competitive learning (KCL) algorithms based on the concept of Varshavsky et al. [18 R. Varshavsky, A. Gottlieb, M. Linial, and D. Horn, Novel unsupervised feature filtering of bilogical data, Bioinformatics 22 (2006), pp. 507–513.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. Integrating the weighted fuzzy c-means (FCM) algorithm with KCL, in this paper, we propose a weighted fuzzy KCL (WFKCL) algorithm. The goal of the proposed WFKCL algorithm is to reduce the clustering error rate when data contain some noise variables. Compared with the k-means, FCM and KCL with existing variable-weight methods, the proposed WFKCL algorithm with the proposed SVD's weight method provides a better clustering performance based on the error rate criterion. Furthermore, the complexity of the proposed SVD's approach is less than Pal et al. [17 S.K. Pal, R.K. De, and J. Basak, Unsupervised feature evaluation: a neuro-fuzzy approach, IEEE. Trans. Neural Netw. 11 (2000), pp. 366–376.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], Wang et al. [19 X.Z. Wang, Y.D. Wang, and L.J. Wang, Improving fuzzy c-means clustering based on feature-weight learning, Pattern Recognit. Lett. 25 (2004), pp. 1123–1132.[Crossref], [Web of Science ®] , [Google Scholar]] and Hung et al. [9 W. -L. Hung, M. -S. Yang, and D. -H. Chen, Bootstrapping approach to feature-weight selection in fuzzy c-means algorithms with an application in color image segmentation, Pattern Recognit. Lett. 29 (2008), pp. 1317–1325.[Crossref], [Web of Science ®] , [Google Scholar]].     

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.     

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.     

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.     

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]).     

Heteroskedasticity Robust Panel Unit Root Testing Under Variance Breaks in Pooled Regressions

Noting that many economic variables display occasional shifts in their second order moments, we investigate the performance of homogenous panel unit root tests in the presence of permanent volatility shifts. It is shown that in this case the test statistic proposed by Herwartz and Siedenburg (2008 Herwartz, H., Siedenburg, F. (2008). Homogenous panel unit root tests under cross-sectional dependence: Finite sample modifications and the wild bootstrap. Computational Statistics and Data Analysis 53(1):137–150.[Crossref], [Web of Science ®] , [Google Scholar]) is asymptotically standard Gaussian. By means of a simulation study we illustrate the performance of first and second generation panel unit root tests and undertake a more detailed comparison of the test in Herwartz and Siedenburg (2008 Herwartz, H., Siedenburg, F. (2008). Homogenous panel unit root tests under cross-sectional dependence: Finite sample modifications and the wild bootstrap. Computational Statistics and Data Analysis 53(1):137–150.[Crossref], [Web of Science ®] , [Google Scholar]) and its heteroskedasticity consistent Cauchy counterpart introduced in Demetrescu and Hanck (2012a Demetrescu, M., Hanck, C. (2012a). A simple nonstationary-volatility robust panel unit root test. Economics Letters 117(2):10–13.[Crossref], [Web of Science ®] , [Google Scholar]). As an empirical illustration, we reassess evidence on the Fisher hypothesis with data from nine countries over the period 1961Q2–2011Q2. Empirical evidence supports panel stationarity of the real interest rate for the entire subperiod. With regard to the most recent two decades, the test results cast doubts on market integration, since the real interest rate is diagnosed nonstationary.     

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.     

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.     

Records Properties of Non Stationary Time Series

This article proposes an asymptotic expansion for the Studentized linear discriminant function using two-step monotone missing samples under multivariate normality. The asymptotic expansions related to discriminant function have been obtained for complete data under multivariate normality. The result derived by Anderson (1973 Anderson , T. W. ( 1973 ). An asymptotic expansion of the distribution of the Studentized classification statistic W . The Annals of Statistics 1 : 964 – 972 .[Crossref], [Web of Science ®] , [Google Scholar]) plays an important role in deciding the cut-off point that controls the probabilities of misclassification. This article provides an extension of the result derived by Anderson (1973 Anderson , T. W. ( 1973 ). An asymptotic expansion of the distribution of the Studentized classification statistic W . The Annals of Statistics 1 : 964 – 972 .[Crossref], [Web of Science ®] , [Google Scholar]) in the case of two-step monotone missing samples under multivariate normality. Finally, numerical evaluations by Monte Carlo simulations were also presented.     

Inference on locally ordered breaks in multiple regressions

We consider issues related to inference about locally ordered breaks in a system of equations, as originally proposed by Qu and Perron (2007 Qu, Z., Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica 75:459–502.[Crossref], [Web of Science ®] , [Google Scholar]). These apply when break dates in different equations within the system are not separated by a positive fraction of the sample size. This allows constructing joint confidence intervals of all such locally ordered break dates. We extend the results of Qu and Perron (2007 Qu, Z., Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica 75:459–502.[Crossref], [Web of Science ®] , [Google Scholar]) in several directions. First, we allow the covariates to be any mix of trends and stationary or integrated regressors. Second, we allow for breaks in the variance-covariance matrix of the errors. Third, we allow for multiple locally ordered breaks, each occurring in a different equation within a subset of equations in the system. Via some simulation experiments, we show first that the limit distributions derived provide good approximations to the finite sample distributions. Second, we show that forming confidence intervals in such a joint fashion allows more precision (tighter intervals) compared to the standard approach of forming confidence intervals using the method of Bai and Perron (1998 Bai, J., Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica 66:47–78.[Crossref], [Web of Science ®] , [Google Scholar]) applied to a single equation. Simulations also indicate that using the locally ordered break confidence intervals yields better coverage rates than using the framework for globally distinct breaks when the break dates are separated by roughly 10% of the total sample size.     

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.     

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.     

Stochastic Comparisons and Optimal Allocation for Policy Limits and Deductibles

In this article, we discuss about the stochastic comparisons and optimal allocation for policy limits and deductibles. We order the total retained losses of a policyholder in the usual stochastic order under more general conditions of X _i (i = 1,…, n), based on which the optimal allocation of policy limits and deductibles are achieved in some special cases. Several results in Cheung (2007 Cheung , K. C. ( 2007 ). Optimal allocation of policy limits and deductibles . Insur. Math. Econ. 41 : 291 – 382 .[Crossref], [Web of Science ®] , [Google Scholar]) and Lu and Meng (2011 Lu , Z. , Meng , L. ( 2011 ). Stochastic comparisons for allocations of policy limits and deductibles with applications . Insur. Math. Econ. 48 : 338 – 343 .[Crossref], [Web of Science ®] , [Google Scholar]) are generalized here.     

Local influence diagnostics for generalized linear mixed models with overdispersion

Since the seminal paper by Cook and Weisberg [9 R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman &; Hall, London, 1982. [Google Scholar]], local influence, next to case deletion, has gained popularity as a tool to detect influential subjects and measurements for a variety of statistical models. For the linear mixed model the approach leads to easily interpretable and computationally convenient expressions, not only highlighting influential subjects, but also which aspect of their profile leads to undue influence on the model's fit [17 E. Lesaffre and G. Verbeke, Local influence in linear mixed models, Biometrics 54 (1998), pp. 570–582. doi: 10.2307/3109764[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. Ouwens et al. [24 M.J.N.M. Ouwens, F.E.S. Tan, and M.P.F. Berger, Local influence to detect influential data structures for generalized linear mixed models, Biometrics 57 (2001), pp. 1166–1172. doi: 10.1111/j.0006-341X.2001.01166.x[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] applied the method to the Poisson-normal generalized linear mixed model (GLMM). Given the model's nonlinear structure, these authors did not derive interpretable components but rather focused on a graphical depiction of influence. In this paper, we consider GLMMs for binary, count, and time-to-event data, with the additional feature of accommodating overdispersion whenever necessary. For each situation, three approaches are considered, based on: (1) purely numerical derivations; (2) using a closed-form expression of the marginal likelihood function; and (3) using an integral representation of this likelihood. Unlike when case deletion is used, this leads to interpretable components, allowing not only to identify influential subjects, but also to study the cause thereof. The methodology is illustrated in case studies that range over the three data types mentioned.     

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.     

Bivariate Continuous Distributions with Specified Conditional Hazard Functions

Analysis of covariance (ANCOVA) is the standard procedure for comparing several treatments when the response variable depends on one or more covariates. We consider the problem of testing the equality of treatment effects when the variances are not assumed to be equal. It is well known that classical F test is not robust with respect to the assumption of equal variances and may lead to misleading conclusions if the variances are not equal. Ananda (1998 Ananda , M. M. A. ( 1998 ). Bayesian and non-Bayesian solutions to analysis of covariance models under heteroscedasticity . J. Econometrics 86 : 177 – 192 .[Crossref], [Web of Science ®] , [Google Scholar]) developed a generalized F test for testing the equality of treatment effects. However, simulation studies show that the actual size of this test can be much higher than the nominal level when the sample sizes are small, particularly when the number of treatments is large. In this article, we develop a test using the parametric bootstrap approach of Krishnamoorthy et al. (2007 Krishnamoorthy , K. , Lu , F. , Mathew , T. ( 2007 ). A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models . Computat. Statist. Data Anal. 51 : 5731 – 5742 .[Crossref], [Web of Science ®] , [Google Scholar]). Our simulations show that the actual size of our proposed test is close to the nominal level, irrespective of the number of treatments and sample sizes. Our simulations also indicate that our proposed PB test is more robust, with respect to the assumption of normality, than the generalized F test. Therefore, our proposed PB test provides a satisfactory alternative to the generalized F test.     

On the optimal allocation of active redundancies in series system

This paper studies the allocations of two non identical active redundancies in series systems in terms of the reversed hazard rate order and hazard rate order, which generalizes some results built in Valdés and Zequeira (2003 Valdés, J. E., and R. I. Zequeira 2003. On the optimal allocation of an active redundancy in a two-component series system. Stat. Probab. Lett. 63:325–32.[Crossref], [Web of Science ®] , [Google Scholar], 2006 Valdés, J. E., and R. I. Zequeira 2006. On the optimal allocation of two active redundancies in a two-component series system. Oper. Res. Lett. 34:49–52.[Crossref], [Web of Science ®] , [Google Scholar]).     

Two-sided Confidence Bands with the Inferential Sensitivity of One-Sided Bands

In this article, we consider investigating whether any of k treatments are better than a control under the assumption of each treatment mean being no less than the control mean. A classic problem is to find the simultaneous confidence bounds for the difference between each treatment and the control. Compared with hypothesis testing, confidence bounds have the attractive advantage of telling more information about the effective treatment. Generally, the one-sided lower bounds are provided as it's enough for detecting effective treatment and the one-sided lower bounds has sharper lower bands than two-sided ones. However, a two-sided procedure provides both upper and lower bounds on the differences. In this article, we develop a new procedure which combines the good aspects of both the one-sided and the two-sided procedures. This new procedure has the same inferential sensitivity of the one-sided procedure proposed by Zhao (2007 Zhao , H. B. ( 2007 ). Comparing several treatments with a control . J. Statist. Plann. Infer. 137 : 2996 – 3006 .[Crossref], [Web of Science ®] , [Google Scholar]) while also providing simultaneous two-sided bounds for the differences between treatments and the control. By our computation results, we find the new procedure is better than Hayter, Miwa and Liu's procedure (Hayter et al., 2000 Hayter , A. J. , Miwa , T. , Liu , W. ( 2000 ). Combining the advantages of one-sided and two-sided procedures for comparing several treatments with a control . J. Statist. Plann. Infer. 86 : 81 – 99 .[Crossref], [Web of Science ®] , [Google Scholar]), when the sample size is balanced. We also illustrate the new procedure by an example.