On the Choice of Nonparametric Entropy Estimator in Entropy-Based Goodness-of-Fit Test Statistics

Entropy-based goodness-of-fit test statistics can be established by estimating the entropy difference or Kullback–Leibler information, and several entropy-based test statistics based on various entropy estimators have been proposed. In this article, we first give comments on some problems resulting from not satisfying the moment constraints. We then study the choice of the entropy estimator by noting the reason why a test based on a better entropy estimator does not necessarily provide better powers.     

Predictive Influence of Unavailable Values of Future Explanatory Variables in a Linear Model

We consider an approach to prediction in linear model when values of the future explanatory variables are unavailable, we predict a future response y ^f at a future sample point x ^f when some components of x ^f are unavailable. We consider both the cases where x ^f are dependent and independent but normally distributed. A Taylor expansion is used to derive an approximation to the predictive density, and the influence of missing future explanatory variables (the loss or discrepancy) is assessed using the Kullback–Leibler measure of divergence. This discrepancy is compared in different scenarios including the situation where the missing variables are dropped entirely.     

Full Bayesian Analysis for a Model of Tail Dependence

The family of the asymmetric logistic copulas appears naturally in modeling tail dependence. Within this family, some well-known models, as independence and logistic dependence, define precise hypotheses, having zero posterior probability for an absolute continuous posterior distribution.

We show that the e-value associated to the Full Bayesian Significance Test has a good performance in non standard dependence problems, obtaining posterior estimates and predictive distributions.

The analysis proposed is illustrated with two examples: (1) monthly sea level maxima at Newlyn and Sheerness, England (1990–2005) and (2) AIDS rates related to an educational indicator in U.S. Census Bureau (2007 U.S. Census Bureau (2007). Persons 25 Years Old and Over with a Bachelor's Degree or More. http://www.census.gov/statab/ranks/rank19.html  [Google Scholar]). We validate the inferences obtained through simulated data.     

Adaptive Procedures for the Wilcoxon–Mann–Whitney Test: Seven Decades of Advances

The Wilcoxon–Mann–Whitney test has dominated non parametric analyses in behavioral sciences for the past seven decades. Its widespread use masks the fact that there exist simple “adaptive” procedures which use data-dependent statistical decision rules to select an optimal non parametric test. This paper discusses key adaptive approaches for testing differences in locations in two-sample environments. Our Monte Carlo analysis shows that adaptive procedures often perform substantially better than t-tests, even with moderately sized samples (80 observations). We illustrate adaptive approaches using data from Gneezy and Smorodinsky (2006 Gneezy, U., Smorodinsky, R. (2006). All-pay auctions: an experimental study. J. Economic Behav. Organizat. 61(2): 255275.[Crossref], [Web of Science ®] , [Google Scholar]), and offer a Stata package to researchers interested in taking advantage of these techniques.     

国际油气价格与汇率动态相依关系研究:基于一种新的时变最优Copula模型

本文提出一个新的时变最优Copula模型,可以准确识别二元时间序列任意时点最优的相依结构。该模型构造了半旋转copula以刻画非对称的反向相依关系,并引入独立性的无分布检验证实相依关系的存在性。同时,我们对能源商品市场（原油、天然气）、外汇市场间动态相依关系进行了实证分析,实证结果表明跨市场相依结构类型确实是时变的,突发事件往往是相依结构突变的主因。另外,时变最优Copula模型的主要优势在于不仅能够捕捉相依方向和相依强度的动态性,还能有效捕捉相依结构类型的动态性。     

Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach

In this paper, maximum likelihood and Bayes estimators of the parameters, reliability and hazard functions have been obtained for two-parameter bathtub-shaped lifetime distribution when sample is available from progressive Type-II censoring scheme. The Markov chain Monte Carlo (MCMC) method is used to compute the Bayes estimates of the model parameters. It has been assumed that the parameters have gamma priors and they are independently distributed. Gibbs within the Metropolis–Hasting algorithm has been applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and highest posterior density credible intervals of the unknown parameters as well as reliability and hazard functions have been computed. The results of Bayes estimators are obtained under both the balanced-squared error loss and balanced linear-exponential (BLINEX) loss. Moreover, based on the asymptotic normality of the maximum likelihood estimators the approximate confidence intervals (CIs) are obtained. In order to construct the asymptotic CI of the reliability and hazard functions, we need to find the variance of them, which are approximated by delta and Bootstrap methods. Two real data sets have been analyzed to demonstrate how the proposed methods can be used in practice.     

Errors-in-variables beta regression models

Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0, 1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error. The structural approach, in which the covariates measured with error are assumed to be random variables, is employed. Three estimation methods are presented, namely maximum likelihood, maximum pseudo-likelihood and regression calibration. Monte Carlo simulations are used to evaluate the performance of the proposed estimators and the naïve estimator. Also, a residual analysis for beta regression models with measurement errors is proposed. The results are illustrated in a real data set.     

Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density

We investigate the issue of bandwidth estimation in a functional nonparametric regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the recent work of Shang (2013 Shang, H.L. (2013), ‘Bayesian Bandwidth Estimation for a Nonparametric Functional Regression Model with Unknown Error Density’, Computational Statistics &; Data Analysis, 67, 185–198. doi: 10.1016/j.csda.2013.05.006[Crossref], [Web of Science ®] , [Google Scholar]) [‘Bayesian Bandwidth Estimation for a Nonparametric Functional Regression Model with Unknown Error Density’, Computational Statistics &; Data Analysis, 67, 185–198], we approximate the unknown error density by a kernel density estimator of residuals, where the regression function is estimated by the functional Nadaraya–Watson estimator that admits mixed types of regressors. We derive a likelihood and posterior density for the bandwidth parameters under the kernel-form error density, and put forward a Bayesian bandwidth estimation approach that can simultaneously estimate the bandwidths. Simulation studies demonstrated the estimation accuracy of the regression function and error density for the proposed Bayesian approach. Illustrated by a spectroscopy data set in the food quality control, we applied the proposed Bayesian approach to select the optimal bandwidths in a functional nonparametric regression model with mixed types of regressors.