In the classical theory of Edgeworth expansion for the sample mean, it is typically assumed that the sampling distribution is either lattice valued or is sufficiently smooth to satisfy Cramér's regularity condition. However, applications of Edgeworth expansions to problems involving the...

Let N = {1, 2, ...} and let {Xi:i [set membership, variant] Nd1} and {Yj:j [set membership, variant] Nd2} be two families of i.i.d. integrable random variables. Let S(nA) be the sum of those XiYj's for which A [subset of] [0,1]d, d = d1 + d2 and (i/n,,j/n) [set membership, variant] A. It is...

Test statistics are proposed for testing equality of two p-variate probability density functions. The statistics are based on the integrated square distance between two kernel-based density estimates and are two-sample versions of the statistic studied by Hall (1984, J. Multivariate Anal. 14...

This paper is concerned with the asymptotic relative efficiency of the Gaussian and least squares estimators when employed to estimate the parameters of vector ARMA models presented in echelon canonical form. The relative efficiency is assessed via the variance-covariance matrices of the...

In this note, we establish law of the logarithm for kernel-type density and hazard rate estimators based on censored data. These results are applied to get optimal bandwidths with respect to strong uniform consistency.

Our main result is the existence and uniqueness of an invariant measure for reflected Brownian motion (RBM) in a wedge that is transient to [infinity]. We also consider this question for RBM that has been killed at the corner of the wedge.

Several conditions are established under which a family of elliptical probability density functions possesses a preferable consistency property. The consistency property ensures that any marginal distribution of a random vector whose distribution belongs to a specific elliptical family also...

The aim of the present paper is to clarify the rôle of extreme order statistics in general statistical models. This is done within the general setup of statistical experiments in LeCam's sense. Under the assumption of monotone likelihood ratios, we prove that a sequence of experiments is...

We study the bootstrap distribution for U-statistics with special emphasis on the degenerate case. For the Efron bootstrap we give a short proof of the consistency using Mallows' metrics. We also study the i.i.d. weighted bootstrap [formula] where (Xi) and ([xi]i) are two i.i.d. sequences,...

Rates of convergence for nonparametric regression estimators based on recursive partitioning schemes are derived. The central idea is to consider the tree-structured regression estimator as a wavelet estimator based on the orthogonal system of Haar functions. A locally adaptive data-driven...