The Bayes rule of the variance parameter of the hierarchical normal and inverse gamma model under Stein's loss

For the variance parameter of the hierarchical normal and inverse gamma model, we analytically calculate the Bayes rule (estimator) with respect to a prior distribution IG (alpha, beta) under Stein's loss function. This estimator minimizes the posterior expected Stein's loss (PESL). We also analytically calculate the Bayes rule and the PESL under the squared error loss. Finally, the numerical simulations exemplify that the PESLs depend only on alpha and the number of observations. The Bayes rules and PESLs under Stein's loss are unanimously smaller than those under the squared error loss.     

Bivariate,multivariate, and matrix variate normal characterizations: A brief survey II

The paper entitled “Bivariate and Multivariate Normal Characterizations: A Brief Survey,” by Hamedani, which was published in 1992, covered the published characterizations of bivariate and multivariate normal (MVN) distributions from 1941 to 1991. The present work is a follow-up to the 1991/1992 survey which includes not only characterizations of the bivariate and MVN distributions, but also characterizations of the matrix variate normal distribution, which have appeared from 1991/1992 to the present.     

Pairwise comparisons of treatments with ordinal responses in a two-way setting

In clinical studies, pairwise comparisons are frequently performed to examine differences in efficacy between treatments. The statistical methods of pairwise comparisons are available when treatment responses are measured on an ordinal scale. The Wilcoxon–Mann–Whitney test and the latent normal model are popular examples. However, these procedures cannot be used to compare treatments in parallel groups (a two-way design) when overall type I error must be controlled. In this paper, we explore statistical approaches to the pairwise testing of treatments that satisfy the requirements of a two-way layout. The results of our simulation indicate that the latent normal approach is superior to the Wilcoxon–Mann–Whitney test. Clinical examples are used to illustrate our suggested testing methods.     

The Peasant World in the Discourse of Generational Sorrow

This article spells out the methodological considerations and various procedural and methodological subtleties developed over the author's quarter century of sociological field studies of Russia's peasant worlds. Particular attention is paid to “voices from below”—peasant discursive formats that capture, in natural and undiluted form, the evolution of peasant practices constituting the core of everyday life. In particular, the phenomenon of generational sorrow and a special chronological nostalgia that functions as a “social gyroscope” is identified and discursively captured. This phenomenon is noteworthy and useful for its ability to retain a record of the productively longed for past in a rural community's collective memory and thereby influence new peasant worlds taking shape today.     

Comparison of dichotomized and distributional approaches in rare event clinical trial design: a fixed Bayesian design

This research was motivated by our goal to design an efficient clinical trial to compare two doses of docosahexaenoic acid supplementation for reducing the rate of earliest preterm births (ePTB) and/or preterm births (PTB). Dichotomizing continuous gestational age (GA) data using a classic binomial distribution will result in a loss of information and reduced power. A distributional approach is an improved strategy to retain statistical power from the continuous distribution. However, appropriate distributions that fit the data properly, particularly in the tails, must be chosen, especially when the data are skewed. A recent study proposed a skew-normal method. We propose a three-component normal mixture model and introduce separate treatment effects at different components of GA. We evaluate operating characteristics of mixture model, beta-binomial model, and skew-normal model through simulation. We also apply these three methods to data from two completed clinical trials from the USA and Australia. Finite mixture models are shown to have favorable properties in PTB analysis but minimal benefit for ePTB analysis. Normal models on log-transformed data have the largest bias. Therefore we recommend finite mixture model for PTB study. Either finite mixture model or beta-binomial model is acceptable for ePTB study.     

A new generalized two-sided class of distributions with an emphasis on two-sided generalized normal distribution

The ordinary-G class of distributions is defined to have the cumulative distribution function (cdf) as the value of the cdf of the ordinary distribution F whose range is the unit interval at G, that is, F(G), and it generalizes the ordinary distribution. In this work, we consider the standard two-sided power distribution to define other classes like the beta-G and the Kumaraswamy-G classes. We extend the idea of two-sidedness to other ordinary distributions like normal. After studying the basic properties of the new class in general setting, we consider the two-sided generalized normal distribution with maximum likelihood estimation procedure.     

Likelihood procedure for testing changes in skew normal model with applications to stock returns

The skew normal distribution family is an attractive distribution family due to its mathematical tractability and inclusion of the normal distribution as the special case. It has wide applications in many applied fields such as finance, economics, and medical research. Such a distribution family has been studied extensively since it was introduced by Azzalini in 1985 Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12:171–178. [Google Scholar] for the first time. Yet, few work has been done on the study of change point problem related to this distribution family. In this article, we propose the likelihood ratio test (LRT) to detect changes in the parameters of the skew normal distribution associated with some asymptotic results of the test statistic. Simulations have been conducted under different scenarios to investigate the performance of the proposed method. Comparisons to some other existing method indicate the comparable power of the method in detecting changes in parameters of the skew normal distribution model. Applications on two real data: Brazilian and Tanzanian stock returns illustrate the detection procedure.     

Bootstrap methods for multivariate hypothesis testing

The nonparametric and parametric bootstrap methods for multivariate hypothesis testing are developed. They are used to approximate the null distribution of the test statistics proposed by Duchesne and Francq (2015 Duchesne, P., Francq, C. (2015). Multivariate hypothesis testing using generalized and {2}-inverses—with applications. Statistics 49:475–496.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), resulting in bootstrap testing procedures. In the problem of testing for the mean vector of a multivariate distribution, the asymptotic validity of the bootstrap methods is proved. The finite sample performance of the new solutions is demonstrated by means of Monte Carlo simulation studies. They indicate that for small-sample size, the bootstrap tests provide a better finite sample properties than the asymptotic tests considered by Duchesne and Francq (2015 Duchesne, P., Francq, C. (2015). Multivariate hypothesis testing using generalized and {2}-inverses—with applications. Statistics 49:475–496.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]).     

Bootstrap approach to test the homogeneity of order restricted mean vectors when the covariance matrices are unknown

Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are unknown, arbitrary positive definite and unequal are considered. This problem of testing has been studied to some extent, for example, by Kulatunga and Sasabuchi (1984 Kulatunga, D. D. S., Sasabuchi, S. (1984). A test of homogeneity of mean vectors against multivariate isotonic alternatives. Mem Fac Sci, Kyushu Univ Ser A Mathemat 38:151–161. [Google Scholar]) when the covariance matrices are known and also Sasabuchi et al. (2003 Sasabuchi, S., Tanaka, K., Tsukamodo, T. (2003). Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. Annals of Statistics. 31(5):1517–1536.[Web of Science ®] , [Google Scholar]) and Sasabuchi (2007 Sasabuchi, S. (2007). More powerful tests for homogeneity of multivariate normal mean vectors under an order restriction. Sankhya 69(4):700–716. [Google Scholar]) when the covariance matrices are unknown but common. In this paper, a test statistic is proposed and because of the main advantage of the bootstrap test is that it avoids the derivation of the complex null distribution analytically, a bootstrap test statistic is derived and since the proposed test statistic is location invariance the bootstrap p-value defined logical and some steps are presented to estimate it. Our numerical studies via Monte Carlo simulation show that the proposed bootstrap test can correctly control the type I error rates. The power of the test for some of the p-dimensional normal distributions is computed by Monte Carlo simulation. Also, the null distribution of test statistic is estimated using kernel density. Finally, the bootstrap test is illustrated using a real data.     

The beta skew-generalized normal distribution

In this article, we develop the skew-generalized normal distribution introduced by Arellano-Valle et al. (2004 Arellano-Valle, R.B., Gomez, H.W., Quintana, F.A. (2004). A new class of skew-normal distribution. Commun. Stat. - Theory Methods. 33(7):1465–1480.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) to a new family of the Beta skew-generalized normal (BSGN) distribution . Here, we present some theorems and properties of BSGN distribution and obtain its moment-generating function.