This paper studies the asymptotic behavior of the least squares estimators in segmented multiple regression. For a model with more than one partitioning variable, each of which has one or more change-points, we study the asymptotic properties of the estimated change-points and regression...

While the noncentral Wishart distribution is generally introduced as the distribution of the random symmetric matrix where Y1,...,Yn are independent Gaussian rows in with the same covariance, the present paper starts from a slightly more general definition, following the extension of the...

In this paper we consider robust parameter estimation based on a certain cross entropy and divergence. The robust estimate is defined as the minimizer of the empirically estimated cross entropy. It is shown that the robust estimate can be regarded as a kind of projection from the viewpoint of a...

Consider the problem of estimating the mean vector [theta] of a random variable X in , with a spherically symmetric density f(||x-[theta]||2), under loss ||[delta]-[theta]||2. We give an increasing sequence of bounds on the shrinkage constant of Stein-type estimators depending on properties of...

In this paper, the problem of estimating the precision matrix of a multivariate Kotz type model is considered. First, using the quadratic loss function, we prove that the unbiased estimator , where denotes the sample sum of product matrix, is dominated by a better constant multiple of , denoted...

We construct a broad class of generalized Bayes minimax estimators of the mean of a multivariate normal distribution with covariance equal to [sigma]2Ip, with [sigma]2 unknown, and under the invariant loss ||[delta](X)-[theta]||2/[sigma]2. Examples that illustrate the theory are given. Most...

Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established in the iid Gaussian case. Our work uses the approach that generalizes the one used in [A. Munk, Bissantz, T. Wagner, G. Freitag, On difference based variance...

In this paper we derive rates of uniform strong convergence for the kernel estimator of the regression function in a left-truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary [alpha]-mixing sequence. The estimation of the covariate's...

In this paper, we discuss the estimation of a density function based on censored data by the kernel smoothing method when the survival and the censoring times form a stationary [alpha]-mixing sequence. A Berry-Esseen type bound is derived for the kernel density estimator at a fixed point x. For...

Asymptotic expansions of the distributions of parameter estimators in mean and covariance structures are derived. The parameters may be common to, or specific in means and covariances of observable variables. The means are possibly structured by the common/specific parameters. First, the...