A nonparametric specification test for the volatility functions of diffusion processes

This paper develops a new test for the parametric volatility function of a diffusion model based on nonparametric estimation techniques. The proposed test imposes no restriction on the functional form of the drift function and has an asymptotically standard normal distribution under the null hypothesis of correct specification. It is consistent against any fixed alternatives and has nontrivial asymptotic power against a class of local alternatives with proper rates. Monte Carlo simulations show that the test performs well in finite samples and generally has better power performance than the nonparametric test of Li (2007 Li, F. (2007). Testing the parametric specification of the diffusion function in a diffusion process. Econometric Theory 23(2):221–250.[Crossref], [Web of Science ®] , [Google Scholar]) and the stochastic process-based tests of Dette and Podolskij (2008 Dette, H., Podolskij, M. (2008). Testing the parametric form of the volatility in continuous time diffusion models–a stochastic process approach. Journal of Econometrics 143(1):56–73.[Crossref], [Web of Science ®] , [Google Scholar]). When applying the test to high frequency data of EUR/USD exchange rate, the empirical results show that the commonly used volatility functions fit more poorly when the data frequency becomes higher, and the general volatility functions fit relatively better than the constant volatility function.     

Zero-Inflated NGINAR(1) process

In this paper, we develop a zero-inflated NGINAR(1) process as an alternative to the NGINAR(1) process (Risti?, Nasti?, and Bakouch 2009 Risti?, M. M., A. S. Nasti?, and H. S. Bakouch. 2009. A new geometric first-order integer-valued autoregressive (NGINAR(1)) process. Journal of Statistical Planning and Inference 139:2218–26.[Crossref], [Web of Science ®] , [Google Scholar]) when the number of zeros in the data is larger than the expected number of zeros by the geometric process. The proposed process has zero-inflated geometric marginals and contains the NGINAR(1) process as a particular case. In addition, various properties of the new process are derived such as conditional distribution and autocorrelation structure. Yule-Walker, probability based Yule-Walker, conditional least squares and conditional maximum likelihood estimators of the model parameters are derived. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Forecasting performances of the model are discussed. Application to a real data set shows the flexibility and potentiality of the new model.     

Nonparametric test for stratum effects in the cox model with interval-censored data

The testing of the stratum effects in the Cox model is an important and commonly asked question in medical research as well as in many other fields. In this paper, we will discuss the problem where one observes interval-censored failure time data and generalize the procedure given in Sun and Yang (2000 Sun, J., and I. Yang. 2000. Nonparametric test for stratum effects in the cox model. Lifetime Data Analysis 6:321–30.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) for right-censored data. The asymptotic distribution of the new test statistic is established and the simulation study conducted for the evaluation of the finite sample properties of the method suggests that the generalized procedure seems to work well for practical situations. An application is provided.     

Bias corrected empirical Bayes confidence intervals for the selected mean

Empirical Bayes (EB) methods are very useful for post selection inference. Following Datta et al. (2002 Datta, G. S., M. Ghosh, D. D. Smith, and P. Lahiri. 2002. On an asymptotic theory of conditional and unconditional coverage probabilities of empirical Bayes confidence intervals. Scandinavian Journal of Statistics 29:139–52.[Crossref], [Web of Science ®] , [Google Scholar]), we construct EB confidence intervals for the selected population mean. The EB intervals are adjusted to achieve the target coverage probabilities asymptotically up to the second order. Both unconditional coverage probabilities of EB intervals and corresponding probabilities conditional on ancillary statistics are found.     

Letter to the Editor

The aim of this letter to acknowledge of priority on calibration estimation. There are numerous studies on calibration estimation in literature. The studies on calibration estimation are reviewed and it is found out that an existing calibration estimator is reprocessed in the recent paper published by Nidhi et al. (2007 Nidhi, B. V. S. Sisodia, Subedar Singh, and Sanjay K. Singh. 2017. Calibration approach estimation of the mean in stratified sampling and stratified double sampling. Commun.Statist.Theor.Meth. 46 (10):4932–4942.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]).     

Complete integral convergence for arrays of row-wise extended independent random variables under Sub-linear expectations

Abstract

In this paper, we establish the complete convergence and complete integral convergence for arrays of row-wise extended independent random variables under sub-linear expectation space with some conditions. At the same time we extend some complete convergence and complete integral convergence theorems from the classical probability space to the sub-linear expectation space. The results generalize corresponding results obtained by Wu et al. (2017 Zhang, L. X. 2016b. Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm. Science China Mathematics 59 (12):2503–26. doi: 10.1007/s11425-016-0079-1.[Crossref], [Web of Science ®] , [Google Scholar]).     

The Johnson System of Frequency Curves—Historical,Graphical, and Limiting Perspectives

Abstract

The idea of transforming one random variate to another with a more convenient density has been developed in the first half of the 20th century. In his thesis, Norman L. Johnson (1917–2004) developed a pioneering system of transformations of the standard normal distribution which gained substantial popularity in the second half of the 20th century and beyond. In Johnson’s 1949 Johnson, N. L. (1949), “Systems of Frequency Curves Generated by Methods of Translation,” Biometrika, 36, 149–176.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar] Biometrika paper entitled Systems of frequency curves generated by methods of translation, summarizing that thesis, one of his primary interests was the behavior of the shape of the probability density functions as their parameter values change. Herein, we attempt to further elucidate this behavior through a series of geometric expositions of that transformation process. In these expositions insight is obtained into the behavior of Johnson’s density functions, and their skewness and kurtosis, as they converge to their limiting distributions, a topic which received little attention.     

Testing economic “genetic pleiotropy” for Box-Cox linear model

Abstract

Genetic pleiotropy occurs when a single gene influences two or more seemingly unrelated phenotypic traits. It is significant to detect pleiotropy and understand its causes. However, most current statistical methods to discover pleiotropy mainly test the null hypothesis that none of the traits is associated with a variant, which departures from the null to test just one associated trait or k associated traits. Schaid et al. (2016 Schaid, D. J., X. Tong, B. Larrabee, R. B. Kennedy, G. A. Poland, and J. P. Sinnwell. 2016. Statistical methods for testing genetic pleiotropy. Genetics 204 (2):483–97. doi:10.1534/genetics.116.189308.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) first proposed a sequential testing framework to analyze pleiotropy based on a linear model and a multivariate normal distribution. In this paper, we analyze the Economic pleiotropy which occurs when an economic action or policy influences two or more economic phenomena. In this paper, we extend the linear model to Box-Cox transformation model and proposed a new decision method. It improves the efficiency of hypothesis test and controls the Type I error. We then apply the method using economic data to multivariate sectoral employments in response to governmental expenditures and provide a quantitative assessment and some insights of different impacts from economic policy.     

Estimation of nonseparable models with censored dependent variables and endogenous regressors

In this article we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalize the identification argument put forward in Altonji, Ichimura, and Otsu (2012 Altonji, J. G., Ichimura, H., Otsu, T. (2012). Estimating derivatives in nonseparable models with limited dependent variables. Econometrica 80:1701–1719.[Crossref], [Web of Science ®] , [Google Scholar]), construct a nonparametric estimator, characterize its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. Identification is constructive and is achieved through a control function approach. We show that the estimator is consistent and asymptotically normally distributed. The Monte Carlo results are encouraging.     

On high-dimensional tests for mutual independence based on Pearson’s correlation coefficient

Abstract

This paper investigates a class of statistics based on Pearson’s correlation coefficient for testing the mutual independence of a random vector in high dimensions. Two existing statistics, proposed by Schott (2005 Schott, J. R. 2005. Testing for complete independence in high dimensions. Biometrika 92 (4):951–6. doi:10.1093/biomet/92.4.951.[Crossref], [Web of Science ®] , [Google Scholar]) and Mao (2014 Mao, G. 2014. A new test of independence for high-dimensional data. Statistics & Probability Letters 93:14–8. doi:10.1016/j.spl.2014.05.024.[Crossref], [Web of Science ®] , [Google Scholar]) respectively, are special cases of the class. A generic testing theory for the class of statistics is developed, which clarifies under what conditions the class of statistics can be employed for the testing purpose. By virtue of the theory, three new tests are introduced, and related statistical properties are discussed. To examine our theoretical findings and check the performance of the new tests, simulation studies are applied. The simulation results justify the theoretical findings and show that the newly introduced tests perform well, as long as both the dimension and the sample size of the data are moderately large.     

Comments on “On the weighted mixed Liu-type estimator under unbiased stochastic restrictions”

We make some comments about the paper of Yildiz (2017 Yildiz, N. 2017. On the weighted mixed Liu-type estimator under unbiased stochastic restrictions. Communications in Statistics Simulation and Computation 46 (9):7238–48. do?:10.1080/03610918.2016.1235189.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and correct the theorems in that paper.     

Adaptive estimation for varying coefficient models with nonstationary covariates

In this paper, the adaptive estimation for varying coefficient models proposed by Chen, Wang, and Yao (2015 Chen, Y., Q. Wang, and W. Yao. 2015. Adaptive estimation for varying coefficient models. Journal of Multivariate Analysis 137:17–31.[Crossref], [Web of Science ®] , [Google Scholar]) is extended to allowing for nonstationary covariates. The asymptotic properties of the estimator are obtained, showing different convergence rates for the integrated covariates and stationary covariates. The nonparametric estimator of the functional coefficient with integrated covariates has a faster convergence rate than the estimator with stationary covariates, and its asymptotic distribution is mixed normal. Moreover, the adaptive estimation is more efficient than the least square estimation for non normal errors. A simulation study is conducted to illustrate our theoretical results.     

Survival analysis for a new compounded bivariate failure time distribution in shock and competing risk models via an EM algorithm

Abstract

In this paper, two bivariate models based on the proposed methods of Marshall and Olkin are introduced. In the first model, the new bivariate distribution is presented based on the proposed method of Marshall and Olkin (1967 Marshall, A. W., and I. Olkin. 1967. A multivariate exponential distribution. Journal of the American Statistical Association 62 (317):30–44. doi: 10.2307/2282907.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) which has natural interpretations, and it can be applied in fatal shock models or in competing risks models. In the second model, the proposed method of Marshall and Olkin (1997 Marshall, A. W., and I. Olkin. 1997. A new method of adding a parameter to a family of distributions with application to the exponential and weibull families. Biometrika 84 (3):641–52. doi: 10.1093/biomet/84.3.641.[Crossref], [Web of Science ®] , [Google Scholar]) is generalized to bivariate case and a new bivariate distribution is introduced. We call these new distributions as the bivariate Gompertz (BGP) distribution and bivariate Gompertz-geometric (BGPG) distribution, respectively. Moreover, the BGP model can be obtained as a special case of the BGPG model. Then, we present various properties of the new bivariate models. In this regard, the joint and conditional density functions, the joint cumulative distribution function can be obtained in compact forms. Also, the aging properties and the bivariate hazard gradient are discussed. This model has five unknown parameters and the maximum likelihood estimators cannot be obtained in explicit form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters, and it is computationally quite tractable. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze three real data sets for illustrative purposes.     

Bayesian process monitoring schemes for the two-parameter exponential distribution

In this paper a Bayesian procedure is applied to obtain control limits for the location and scale parameters, as well as for a one-sided upper tolerance limit in the case of the two-parameter exponential distribution. An advantage of the upper tolerance limit is that it monitors the location and scale parameter at the same time. By using Jeffreys’ non-informative prior, the predictive distributions of future maximum likelihood estimators of the location and scale parameters are derived analytically. The predictive distributions are used to determine the distribution of the “run-length” and expected “run-length”. A dataset given in Krishnamoorthy and Mathew (2009 Krishnamoorthy, K., and T. Mathew. 2009. Statistical Tolerance Regions: Theory, Applications and Computation. Wiley Series in Probability and Statistics.[Crossref] , [Google Scholar]) are used for illustrative purposes. The data are the mileages for some military personnel carriers that failed in service. The paper illustrates the flexibility and unique features of the Bayesian simulation method.     

Variance estimation in adaptive cluster sampling

Abstract

In this paper, a class of variance estimator is proposed of a finite population variance under an adaptive cluster sampling design in the presence of information on an auxiliary variable. We obtain expressions for the mean square error and bias for the developed estimators and their performance is evaluated on a Poisson clustered process and a real data set. The simulation study evaluates the efficiency of the suggested estimators for an adaptive cluster sampling (ACS) design and the Isaki (1983 Isaki, C. T. 1983. Variance estimation using auxiliary information. Journal of the American Statistical Association 78 (381):117–23. doi: 10.1080/01621459.1983.10477939.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) estimator of the variance for SRSWOR over the sample variance for SRSWOR.     

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.     

Optimal nonparametric estimator of the area under ROC curve based on clustered data

Abstract

In diagnostic trials, clustered data are obtained when several subunits of the same patient are observed. Intracluster correlations need to be taken into account when analyzing such clustered data. A nonparametric method has been proposed by Obuchowski (1997 Obuchowski, N. A. 1997. Nonparametric analysis of clustered ROC curve data. Biometrics 53 (2):567–78.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) to estimate the Receiver Operating Characteristic curve area (AUC) for such clustered data. However, Obuchowski’s estimator is not efficient as it gives equal weight to all pairwise rankings within and between cluster. In this paper, we propose a more efficient nonparametric AUC estimator with two sets of optimal weights. Simulation results show that the loss of efficiency of Obuchowski’s estimator for a single AUC or the AUC difference can be substantial when there is a moderate intracluster test correlation and the cluster size is large. The efficiency gain of our weighted AUC estimator for a single AUC or the AUC difference is further illustrated using the data from a study of screening tests for neonatal hearing.     

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.     

Analytical results for IGFR and DRPFR distributions,with actuarial applications

An increasing generalized failure rate of a lifetime X defines an ageing concept, denoted by IGFR. Another notion, denoted by DRPFR, is defined by the decreasingness of the reversed proportional failure rate. In this article, we provide characterizations for both IGFR and DRPFR absolutely continuous lifetimes, based on monotonicity of quotients of probabilistic functionals and a result by Nanda and Shaked (2001 Nanda, A.K., Shaked, M. (2001). The hazard rate and the reversed hazard rate orders, with applications to order statistics. Ann. Inst. Stat. Math. 53:853–864.[Crossref], [Web of Science ®] , [Google Scholar]). We derive the necessary conditions for the IGFR notion, based on stochastic orderings of truncated distributions, and we prove that the product of DRPFR lifetimes is also DRPFR; that the IGFR property is preserved by composition with certain risk aversion utility functions; and that the order statistics and the records (and the subsequent order statistic (record)) are IGFR under suitable assumptions, with similar results for DRPFR lifetimes. Also, we provide sufficient conditions for the hazard rate ordering of products and random products of IGFR lifetimes, and similar results for the reversed hazard rate order and DRPFR lifetimes, with a complementary result for the mean residual life order of random products of two families of IGFR lifetimes, we derive the upper and lower bounds for the cumulative distribution function of the product of IGFR lifetimes, and we provide the lower bounds for the risk function of an IGFR lifetime based on the distribution moments, and these bounds are extended for the product of IGFR lifetimes. We discuss extensively the applications of the results in insurance portfolios.     

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.