We give general matrix Studentisation results for random vectors converging in distribution to a spherically symmetric random vector, which have wide applicability to the asymptotic properties of estimators obtained from estimating equations, for example. Appropriate matrix "square roots,"...

LetZ1, ..., Znbe a random sample of sizen[greater-or-equal, slanted]2 from ad-variate continuous distribution functionH, and letVi, nstand for the proportion of observationsZj,j[not equal to]i, such thatZj[less-than-or-equals, slant]Zicomponentwise. The purpose of this paper is to...

We obtain some new results on normalized spacings of independent exponential random variables with possibly different scale parameters. It is shown that the density functions of the individual normalized spacings in this case are mixtures of exponential distributions and, as a result, they are...

Nonparametric estimation of conditional mean functions has been studied extensively in the literature. This paper addresses the question of how to use extra informations to improve the estimation. Particularly, we consider the situation that the conditional mean functionE(ZX) is of interest and...

Forn[greater-or-equal, slanted]2, let ([mu]x[tau], n)[tau][greater-or-equal, slanted]0be the distributions of the Brownian motion on the unit sphereSn[subset of]n+1starting in some pointx[set membership, variant]Sn. This paper supplements results of Saloff-Coste concerning the rate of...

For a sequence of partial sums ofd-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results...

In this note we consider some asymptotic properties of empirical mean direction on spheres. We do not require any symmetry for the underlying density. Thus our results provide the framework for an asymptotic inference regarding mean direction under very weak model assumptions. Mean direction is...

In the GMANOVA model or equivalent growth curve model, shrinkage effects on the MLE (maximum likelihood estimator) are considered under an invariant risk matrix. We first study the fundamental structure of the problem through which we decompose the estimation problem into some conditional...

In this paper, several recursive algorithms for computingM-estimates in multivariate linear regression models are discussed. It is shown that the recursiveM-estimators of regression coefficient and scatter parameters are strongly consistent. In particular, the asymptotic normality of the...

For given observations we consider the resampling distribution obtained by permuting residuals versus thedistribution of errors conditional on their order statistics. We observe thatwith high probabilityboth are approximately equal oncontrast vectorsafter suitable normalization. No...