Entropy inequalities for some multivariate distributions

AbstractIn this paper, we derive some monotonicity properties of generalized entropy functionals of various multivariate distributions. These include the distributions of random eigenvalues arising in many hypothesis testing problems in multivariate analysis; the multivariate Liouville distributions; and the noncentral Wishart distributions

Analysis of compositions of microbiomes with bias correction

Differential abundance analysis of microbiome data continues to be challenging due to data complexity. The authors propose a method which estimates the unknown sampling fractions and corrects the bias induced by their differences among samples

Parameter Estimation in Linear Models with Heteroscedastic Variances Subject to Order Restrictions

Estimation of parameters in linear fixed and mixed effects models, under order restrictions on the error variances, is considered in this article. For simplicity of exposition, we shall assume that the error variances are subject to simple order restriction. Similar methodology can be developed for other forms of order restrictions as well.fixed effects heteroscedastic errors isotonic regression maximum likelihood estimation mixed effects simple order restriction

Qualms about BCa bootstrap confidence intervals

Following the comments of Schenker (1985), Efron (1987) introduced the BCa methodology to construct confidence intervals. In this article we demonstrate that the BCa confidence intervals can degenerate with a very high probability if a [greater-or-equal, slanted] 0.4. On the other hand, if a is small it is not necessary that the BCa intervals perform better in the sense of the size of the confidence interval and/or the coverage probability. This is illustrated by considering the estimation of confidence intervals for the variance components in a two way analysis of variance model.Acceleration constant BC method BCa method confidence interval degenerate variance components

Entropy inequalities for some multivariate distributions

In this paper, we derive some monotonicity properties of generalized entropy functionals of various multivariate distributions. These include the distributions of random eigenvalues arising in many hypothesis testing problems in multivariate analysis; the multivariate Liouville distributions; and the noncentral Wishart distributions.entropy functionals Liouville distributions multivariate beta distributions Schur-concavity Schur-convexity Selberg's integrals noncentral Wishart distributions