Robust Wald-type tests in GLM with random design based on minimum density power divergence estimators

Statistical Methods & Applications - We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum...     

Bayesian and likelihood-based inference for the bivariate normal correlation coefficient

The paper develops some objective priors for correlation coefficient of the bivariate normal distribution. The criterion used is the asymptotic matching of coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. The paper uses various matching criteria, namely, quantile matching, highest posterior density matching, and matching via inversion of test statistics. Each matching criterion leads to a different prior for the parameter of interest. We evaluate their performance by comparing credible intervals through simulation studies. In addition, inference through several likelihood-based methods have been discussed.     

Constrained Bayes and empirical Bayes estimation under random effects normal ANOVA model with balanced loss function

The paper develops constrained Bayes and empirical Bayes estimators in the random effects ANOVA model under balanced loss functions. In the balanced normal–normal model, estimators of the Bayes risks of the constrained Bayes and constrained empirical Bayes estimators are provided which are correct asymptotically up to O(m^-1)$\mathrm{O}(m^{-1})$, that is the remainder term is o(m^-1)$\mathrm{o}(m^{-1})$, m$m$ denoting the number of strata.     

On aggregation of strongly dependent time series

We consider cross-sectional aggregation of time series with long-range dependence. This question arises for instance from the statistical analysis of networks where aggregation is defined via routing matrices. Asymptotically, aggregation turns out to increase dependence substantially, transforming a hyperbolic decay of autocorrelations to a slowly varying rate. This effect has direct consequences for statistical inference. For instance, unusually slow rates of convergence for nonparametric trend estimators and nonstandard formulas for optimal bandwidths are obtained. The situation changes, when time-dependent aggregation is applied. Suitably chosen time-dependent aggregation schemes can preserve a hyperbolic rate or even eliminate autocorrelations completely.     

On generalized conditional cumulative residual inaccuracy measure

Abstract

Recently, the notion of cumulative residual Rényi’s entropy has been proposed in the literature as a measure of information that parallels Rényi’s entropy. Motivated by this, here we introduce a generalized measure of it, namely cumulative residual inaccuracy of order α. We study the proposed measure for conditionally specified models of two components having possibly different ages called generalized conditional cumulative residual inaccuracy measure. Several properties of generalized conditional cumulative residual inaccuracy measure including the effect of monotone transformation are investigated. Further, we provide some bounds on using the usual stochastic order and characterize some bivariate distributions using the concept of conditional proportional hazard rate model.     

A note on the residual median process

We study the residual median process, defined as the median of those observations which are greater than a number t. Using appropriate limit theorems, it is shown that the stochastic process converges in law to a Gaussian process defined in terms of a Brownian bridge.     

Nonparametric Bayes and empirical Bayes estimation of the population median,with application in finite-population sampling

ABSTRACT

Nonparametric Bayes and empirical Bayes estimators of the population median are provided under Dirichlet process priors. The finite-population sampling is used to estimate the finite-population median under Dirichlet process priors. The asymptotic properties of the estimators are obtained from a frequentist perspective.