This paper proposes an averaged version of singular integral estimators, whose bias achieves higher rates of convergence under smoothing assumptions. We derive exact bias bounds, without imposing smoothing assumptions, which are a basis for deriving the rates of convergence under...

This article proposes compactly supported correlation functions, which parameterize the smoothness of the associated stationary and isotropic random field. The constructions are straightforward, and compact support is relevant for various ends: computationally efficient spatial prediction, fast...

It is well known that the uniformly minimum variance unbiased (UMVU) estimators of the risk and the mean squared error (MSE) matrix proposed in the literature for Stein estimators can take negative values with positive probability. In this paper, improved truncated estimators of the risk, risk...

The problem of nonnegative quadratic estimation of a parametric function [gamma]([beta], [sigma])=[beta]'F[beta]+[summation operator]ri=1 fi[sigma]2i in a general mixed linear model {y, X[beta], V([sigma])=[summation operator]ri=1 [sigma]2iVi} is discussed. Necessary and...

An exact asymptotic formula for the tail probability of a multivariate normal distribution is derived. This formula is applied to establish two asymptotic results for the maximum deviation from the mean: the weak convergence to the Gumbel distribution of a normalized maximum deviation and the...

As the extensions of Tukey's depth, a family of affine invariant depth functions are introduced for multivariate location and dispersion. The location depth functions can be used for the purpose of multivariate ordering. Such kind ordering can retain more information from the original data than...

The estimation of the location parameter of an l1-symmetric distribution is considered. Specifically when a p-dimensional random vector has a distribution that is a mixture of uniform distributions on the l1-sphere, we investigate a general class of estimators of the form [delta]=X+g. Under the...

Each [alpha]-stable distribution can be approximated either by an [alpha]-stable distribution with a discrete Poisson spectrum or by a sum of i.i.d. random vectors. Here we give results on the accuracy that can be achieved under both these ways of approximation. They are purely theoretical and...

Estimation of parameters in linear fixed and mixed effects models, under order restrictions on the error variances, is considered in this article. For simplicity of exposition, we shall assume that the error variances are subject to simple order restriction. Similar methodology can be developed...

In the regression model, we assume that the independent variables are random instead of fixed. Consider the problem of estimating the coverage function of a usual confidence interval for the unknown intercept parameter. In this paper, we consider a case in which the number of unknown parameters...