This paper deals with the distribution of the LR statistic for testing the hypothesis that the smallest eigenvalues of a covariance matrix are equal. We derive an asymptotic null distribution of the LR statistic when the dimension p and the sample size N approach infinity, while the ratio p/N...

In this paper we introduce a family of symmetrised M-estimators of multivariate scatter. These are defined to be M-estimators only computed on pairwise differences of the observed multivariate data. Symmetrised Huber's M-estimator and Dümbgen's estimator serve as our examples. The influence...

A partially linear model is considered when the responses are missing at random. Imputation, semiparametric regression surrogate and inverse marginal probability weighted approaches are developed to estimate the regression coefficients and the nonparametric function, respectively. All the...

The problem of minimax estimation is examined for the linear multivariate statistically indeterminate observation model with mixed uncertainty. The a priori information on the distributions of model parameters is formulated in terms of second-order moment characteristics. It is shown that in the...

In this paper, we consider the problem of testing for parameter changes in time series models based on a moving estimates (ME) test. It is widely accepted that detecting some changes, for instance, those caused by temporary parameter shifts by the existing cusum test is difficult. A MV test with...

In this paper we consider the unit root problem for one rather simple autoregressive model Yt,s=aYt-1,s+bYt,s-1+[var epsilon]t,s on a two-dimensional lattice. We show that the growth of variance of Yt,s is essentially different from corresponding growth in the unit root case for AR(1) or AR(2)...

A new class of bivariate distributions is presented in this paper. The procedure used in this paper is based on a latent random variable with exponential distribution. The model introduced here is of Marshall-Olkin type. A mixture of the proposed bivariate distributions is also discussed. The...

Consider the heteroscedastic model Y=m(X)+[sigma](X)[var epsilon], where [var epsilon] and X are independent, Y is subject to right censoring, m(·) is an unknown but smooth location function (like e.g. conditional mean, median, trimmed mean...) and [sigma](·) an unknown but smooth scale...

The authors study a heteroscedastic partially linear regression model and develop an inferential procedure for it. This includes a test of heteroscedasticity, a two-step estimator of the heteroscedastic variance function, semiparametric generalized least-squares estimators of the parametric and...

In this paper we consider elliptical random vectors in with stochastic representation RAU where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere of and is a non-singular matrix. When R has distribution function in the Weibull...