This paper presents a decomposition for the posterior distribution of the covarianee matrix of normal models under a family of prior distributions when missing data are ignorable and monotone. This decomposition is an extension of Bartlett's decomposition of the Wishart distribution to monotone...

This paper studies a problem of discrimination between two populations with binary variables. The number of variables which can be observed is allowed to tend to infinity. Assuming the Dirichlet process prior, we find necessary and sufficient conditions for asymptotically perfect discrimination...

The condition max1=i=nXTiV-1nXi[formula] 0, where Xi are vectors in Rd and Vn = [summation operator]ni=1XiXTi, is important in the asymptotics of various linear and nonlinear regression models. We call it "quadratic negligibility." It is shown that, when Xi are independent and identically...

Multivariate asymptotic (normal) distributions for eigenvalues and unit-length eigenvectors of sample variance and correlation matrices are derived. Beside the general case, when existence of the (finite) fourth-order moments of the population distribution is assumed, formulae for the asymptotic...

Nonparametric kernel regression estimators of the Nadaraya-Watson type are known to have an undesirable bias behavior. We propose a general technique to improve the bias of any given multivariate nonparametric regression estimator based on the requirement that the identity function should be...

Generalizing the random sequence case, this study defines a k - NN density estimator for random variables with multidimensional lattice points serving as index values. The central result is that under random field stationary and mixing assumptions, as well as standard smoothness postulates, our...

Chen and Robinson's (J. Multivariate Anal.8 190-203 (1989)) recent method of comparison of factors spaces of two related populations is formalized and extended to the case of sums of eigenspaces of two compact self-adjoint operators. The factor subspaces are defined as finite sets of each...

We study the asymptotic bias of the moment estimator [gamma]n for the extreme-value index [gamma] [set membership, variant] 5 under quite natural and general conditions on the underlying distribution function. Furthermore the optimal choice for the sample franction in estimating [gamma] is...

Alexander's (1987, Ann. Probab.15 178-203) central limit theorem for empirical processes on Vapnik-Cervonenkis classes of functions is extended to the case with non-Gaussian stable limits. The corresponding weak laws of large numbers are also established.

For the regression model yi = x'i[xi] + ei, 1 = i = n, with i.i.d. residuals {ei}, we introduce the estimator of [xi] which zeros the weighted U-statistic [summation operator][summation operator] qijK(êi, êj), where qij is a score vector for regression vectors xi and xj. These include some M-...