In this paper, we consider an asymptotic normality problem for a vector stochastic difference equation of the formUn+1=(I+an(B+En)) Un+an(un+en), whereBis a stable matrix, andEn--n0,anis a positive real step size sequence withan--n0, [summation operator][infinity]n=1 an=[infinity],...

We present two methods of constructing multivariate compound distributions and investigate the corresponding infinitely divisible and compound Poisson distributions. We then show that the multivariate compound Poisson distributions can be derived as the limiting distributions of the sums of...

We describe a formal approach to constructing the optimal classification rule for classification analysis with unknown prior probabilities ofKmultivariate normal populations membership. This is done by suggesting a balanced design for the classification experiment and by constructing the optimal...

W. Stute (Ann. Probab.19,No. 2 (1991), 812-825) introduced a class of so-calledU-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. In this paper, we extend the results from the independent case to the dependent case.

Nonparametric regression estimator based on locally weighted least squares fitting has been studied by Fan and Ruppert and Wand. The latter paper also studies, in the univariate case, nonparametric derivative estimators given by a locally weighted polynomial fitting. Compared with traditional...

The accuracy of the binned kernel density estimator is studied for general binning rules. We derive mean squared error results for the closeness of this estimator to both the true density and the unbinned kernel estimator. The binning rule and smoothness of the kernel function are shown to...

We study the asymptotics of maximum-likelihood ratio-type statistics for testing a sequence of observations for no change in parameters against a possible change while some nuisance parameters remain constant over time. We obtain extreme value as well as Gaussian-type approximations for the...

LetX1, ..., Xnbe observations from a multivariate AR(p) model with unknown orderp. A resampling procedure is proposed for estimating the orderp. The classical criteria, such as AIC and BIC, estimate the orderpas the minimizer of the function[formula]wherenis the sample size,kis the order...

In some applications, the mean or median response is linearly related to some variables but the relation to additional variables are not easily parameterized. Partly linear models arise naturally in such circumstances. Suppose that a random sample {(Ti, Xi, Yi),i=1, 2, ..., n} is...

In a multiparameter estimation problem, for first-order efficient estimators, second-order Pitman admissibility, and Pitman closeness properties are studied. Bearing in mind the dominant role of Stein-rule estimators in multiparameter estimation theory, such second-order properties are also...