In this paper, we carry out an in-depth theoretical investigation for inference with missing response and covariate data for general regression models. We assume that the missing data are missing at random (MAR) or missing completely at random (MCAR) throughout. Previous theoretical...

Motivated by the likelihood functions of several incomplete categorical data, this article introduces a new family of distributions, grouped Dirichlet distributions (GDD), which includes the classical Dirichlet distribution (DD) as a special case. First, we develop distribution theory for the...

In this paper skewness and kurtosis characteristics of a multivariate p-dimensional distribution are introduced. The skewness measure is defined as a p-vector while the kurtosis is characterized by a pxp-matrix. The introduced notions are extensions of the corresponding measures of...

In this paper we introduce the least-trimmed squares estimator for multivariate regression. We give three equivalent formulations of the estimator and obtain its breakdown point. A fast algorithm for its computation is proposed. We prove Fisher-consistency at the multivariate regression model...

In this paper, a mixture representation for the joint distribution function of progressively Type-II censored order statistics from heterogeneous distributions is established. Applications of this representation to stochastic orderings and inequalities are then illustrated.

We derive herein the limiting laws for certain stationary distributions of birth-and-death processes related to the classical model of chemical adsorption-desorption reactions due to Langmuir. The model has been recently considered in the context of a hybridization reaction on an oligonucleotide...

Parametric models for tail copulas are being used for modeling tail dependence and maximum likelihood estimation is employed to estimate unknown parameters. However, two important questions seem unanswered in the literature: (1) What is the asymptotic distribution of the MLE and (2) how does one...

The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently and there are slightly varying definitions of GPDs available. In this article we investigate the one from Section 5.1 of Falk et al. [Laws of Small Numbers: Extremes and Rare Events, second ed.,...

Let X~f([short parallel]x-[theta][short parallel]2) and let [delta][pi](X) be the generalized Bayes estimator of [theta] with respect to a spherically symmetric prior, [pi]([short parallel][theta][short parallel]2), for loss [short parallel][delta]-[theta][short parallel]2. We show that if...

For kn-nearest neighbor estimates of a regression Y on X (d-dimensional random vector X, integrable real random variable Y) based on observed independent copies of (X,Y), strong universal pointwise consistency is shown, i.e., strong consistency PX-almost everywhere for general distribution of...