Markov inequalities on ordered linear spaces are tightened through the [alpha]-unimodality of the corresponding measures. Modality indices are studied for various induced measures, including the singular values of a random matrix and the periodogram of a time series. These tools support a...

In this paper we consider the problem of testing the hypothesis about the sub-mean vector. For this propose, the asymptotic expansion of the null distribution of Rao's U-statistic under a general condition is obtained up to order of n-1. The same problem in the k-sample case is also...

The problem of estimating linear functionals based on Gaussian observations is considered. Probabilistic error is used as a measure of accuracy and attention is focused on the construction of adaptive estimators which are simultaneously near optimal under probabilistic error over a collection of...

Estimation of regression functions from independent and identically distributed data is considered. The L2 error with integration with respect to the design measure is used as an error criterion. Usually in the analysis of the rate of convergence of estimates besides smoothness assumptions on...

Simultaneous prediction and parameter inference for the independent Poisson observables model are considered. A class of proper prior distributions for Poisson means is introduced. Bayesian predictive densities and estimators based on priors in the introduced class dominate the Bayesian...

We consider several Bayesian multivariate spatial models for estimating the crash rates from different kinds of crashes. Multivariate conditional autoregressive (CAR) models are considered to account for the spatial effect. The models considered are fully Bayesian. A general theorem for each...

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not...

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator (LSE) for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only...

This paper extends the results in Li and Loken [A unified theory of statistical analysis and inference for variance component models for dyadic data, Statist. Sinica 12 (2002) 519-535] on the statistical analysis of measurements taken on dyads to the situations in which more than one attribute...

In this paper basic statistics for a skew elliptical model are studied. Distributions of the sample mean and covariance are obtained. An unbiased estimate of the scale matrix and an asymptotically unbiased consistent estimate of the location vector are obtained. The null distribution of the...