We obtain rates of convergence of stochastic relaxation (heat bath algorithm) for continuous densities which have the form of bounded perturbations of Gaussian densities. The rates are calculated in the spaces of square integrable functions with respect to these desities in which the operator...

The breakdown slope, as a useful summary measure of local stability for estimators and test statistics, has been studied recently by He, Simpson, and Protnoy (1990, J. Amer. Statist. Assoc., 85). It is shown here that all regression estimates based on residuals alone in linear models have zero...

Let X be an m - p matrix normally distributed with matrix of means B and covariance matrix Im [circle times operator] [Sigma], where [Sigma] is a p - p unknown positive definite matrix. This paper studies the estimation of B relative to the invariant loss function tr . New classes of invariant...

In this paper, we investigate various fourfold Wold-type decompositions of stationary random fields under different hypotheses of commutation properties. Spectral characterizations of the three multiplicities of the innovation subspaces are obtained. The equivalence relations between the weak...

Let E, V be n-, p-dimensional inner product spaces over the real field, let (V, E) be the set of all linear maps of V into E, and let Y be a normal random vector in (V, E) with mean [mu] = 0 and covariance [Sigma]Y such that S1 [square not subset] S2([not equal to] }0{) is the image set, Im...

Multivariate local limit theorems are established for sums of random variables which are in the domain of attraction of a bivariate stable law, when the concept of stability allows different scaling constants in the different components. The results cover the lattice, non-lattice, and jointly...

The Choquet-Deny theorem on an integral equation is extended using an elementary technique based on a certain inequality for exchangeable random variables. Previous proofs for partial results have involved amongst other things the Hewitt-Savage zero-one law and the martingale convergence...

The "prior density for path" (the Onsager-Machlup functional) is defined for solutions of semilinear elliptic type PDEs driven by white noise. The existence of this functional is proved by applying a general theorem of Ramer on the equivalence of measures on Wiener space. As an application, the...

In a multiparameter situation, this paper characterizes priors under which the Bayesian and frequentist Bartlett corrections for the likelihood ratio statistic differ by o(1). The role of Jeffreys' prior in this regard has also been investigated.

A univariate probability distribution which has support in [-1, 1] and is unimodal with respect to 0 has a variance of at most , which is attained only for the uniform distribution. This well-known result is extended to the multivariate case, where the variance is replaced by the generalized or...