An extended growth curve model is considered which, among other things, is useful when linear restrictions exist on the mean in the ordinary growth curve model. The maximum likelihood estimators consist of complicated stochastic expressions. It is shown how, by the aid of fairly elementary...

Let [mu] be a function defined on an interval [a, b] of finite length. Suppose that y1, ..., yn are uncorrelated observations satisfying E(yj) = [mu](tj) and var(yj) = [sigma]2, j = 1, ..., n, where the tj's are fixed design points. Asymptotic (as n -- [infinity]) approximations of the...

Consistent estimators for the reciprocal of the density at a quantile point, which is the derivative of the quantile function, are considered. Rates of convergence of these estimators, depending on the smoothness properties of the density, are obtained. Two different, but natural, estimators of...

This paper examines the performance of several biased, Stein-like and empirical Bayes estimators for the general linear statistical model under conditions of collinearity. A new criterion for deleting principal components, based on an unbiased estimator of risk, is introduced. Using a squared...

Consider a statistical model, given by the distribution of the observation X, conditional on the parameter [theta], and the prior distribution of the parameter [theta]. Let Hx denote the function that maps the prior mean and the prior covariance matrix into the posterior mean and the posterior...

In this work, the fundamental convergence theorems for multivalued martingales are established in Mosco's sense. The notion of epi-martingale is introduced.

We consider the problem of estimating [theta] = ([theta]1,...,[theta]p) under the weighted squared error loss when the observations xi, i = 1, 2, ..., p are independently from negative binomial distributions NB(ri, [theta]i). There has been considerable interest in providing the Stein type...

Asymptotic expansions for the standardized as well as the studentized least squares estimate in multiple linear regression models are obtained without assuming normal errors and under simple assumptions that are easy to check.

We describe a bootstrap method for estimating mean squared error and smoothing parameter in nonparametric problems. The method involves using a resample of smaller size than the original sample. There are many applications, which are illustrated using the special cases of nonparametric density...