Considered is a linear regression model with a one-dimensional control variable and an m-dimensional response variable y. The components of y may be correlated with known covariance matrix. Let B be the covariance matrix of the Gauss-Markoff estimator for the unknown parameter vector of the...

Let [Phi]' be the strong dual of a nuclear Fréchet space [Phi]. In this paper we present regularity properties, weak convergence, and convergence in probability and in mean square of [Phi]'-valued stochastic evolution equations and convolutions with respect to [Phi]'-valued cadlag martingales.

A general Laplace transform and its inverse and their generalizations are considered in this article. This inverse contains the density functions of quadratic expressions in nonsingular as well as singular normal variables and a non-central version of linear functions of gamma variables, among...

For many of the more complex models in statistical genetics and measurement error analysis (such as, e.g., variance component models) robust methods are obviously needed, but as yet hardly used. This is partly due to the fact that the parameters of such models often have an indispensable...

A location-adaptive hybrid of the fixed-bandwidth kernel density estimate and the nearest-neighbor density estimate is introduced in this paper. It is constructed via a simple adhoc truncation and smoothing of nearest-neighbor distance. Simulations show that the hybrid outperforms its parent...

Let Fn and Gn denote the Kaplan-Meier product-limit estimators of lifetime distributions based on two independent samples, and let Fninv and Gninv denote their quantile functions. We consider the corresponding P-P plot Fn(Gninv) and Q-Q plot Fninv(Gn), and establish strong approximations of...

This paper gives rth order Edgeworth expansions (r = 3) for M-estimators of a regression parameter in a simple linear regression model. The regularity conditions used here essentially require the smoothness of some integrals of the score function with respect to the underlying error...

We consider estimation of a location vector in the presence of known or unknown scale parameter in three dimensions. The technique of proof is Stein's integration by parts and it is used to cover several cases (e.g., non-unimodal distributions) for which previous results were known only in the...

Given a fixed line L (in Rn) and a uniform distribution of points (c) on the unit sphere, L(tc), the point of intersection of L and the hyperplane P · c = 0, leads to a mapping Xn : Rn --> R, which is shown to have a Cauchy distribution.

We investigate optimal bounded influence M-estimators in the general normal regression model with respect to different sensitivities. As a result, we answer some open questions in F. R. Hampel et al. (Robust Statistics, Chap. 6, Wiley, New York). Moreover, we examine the relationship among...