Let Fn be an estimator obtained by integrating a kernel type density estimator based on a random sample of size n from smooth distribution function F. A central limit theorem is established for the target statistic Fn(Un) where the underlying random variable form an absolutely regular stationary...

Let W be a p - p matrix distributed according to the Wishart distribution Wp(n, [Phi]) with [Phi] positive definite and n = p. Let ([nu]n/[sigma]2) g be distributed according to the chi-squared distribution [chi]2([nu]n). Consider hierarchical hypotheses H0 [subset of] H1 [subset of] H2 that H0:...

A p - 1 random vector x is said to have a spherical distribution, if for every p - p orthogonal matrix Q, x and Qx have the same distribution. In this paper, some nonparametric goodness of fit Wilcoxon-type tests for sphericity are proposed. Some results on the limiting distributions of the...

In this paper, we show that the exponential bounds for the PP Kolmogorov-Smirnov statistic, the uniform deviation of an empirical process indexed by the indicators of some sets based on m-dimensional projections, are c(P) [lambda](2 + [alpha])(p - 1)m + 2(m - 1) exp(-2[lambda]2), where [alpha]...

In this paper, a1ll admissible linear estimates of the mean matrix [Theta] from the distribution N([Theta]n-m, Im [circle times operator] In) are given under each of the several definitions for admissibility.

Kernel density estimators for discrete multivariate data are investigated, using the notation framework of contingency tables. We derive large sample properties of kernel estimators and the least-squares cross-validation method for choosing the bandwidth, including the asymptotic bias, the mean...

We consider the problem of estimating the sum of squared error loss L = [beta]-[beta]2 of the least-squares esitmator [beta] for [beta], the regression coefficient. The standard estimator L0 is the expected value of L. Here the error variance is assumed to be known. Previous results of Johnstone...

Bivariate failure rates and mean residual lives for nonnegative integer valued discrete variables are defined and examined for the unique determination of the underlying frequency runction. As an application, a bivariate geometric distribution is obtained through a characterization approach...

In this paper, we provide a weighted approximation for the renewal spacing empirical and quantile processes. Some linear bounds for the empirical distribution and quantile functions are also given.

A strong i.i.d. representation is obtained for the product-limit estimator of the survival function based on left truncated and right censored data. This extends the result of Chao and Lo (1988, Ann. Statist.16, 661-668) for truncated data. An improved rate of the approximation is also obtained...