Asymptotics of M-estimators of the regression coefficients in linear models (both scale-variant and scale-invariant) when the number of regression coefficients tends to infinity as the sample size increases are investigated. The main purpose of this study is to establish the asymptotic...

The main result is that if F is an analytic multifunction and Bt is a complex Brownian motion, then F(Bt) is a subholomorphic process. It has previously been shown that such processes enjoy many interesting sample-path properties. As special cases of the theorem above, we recover f holomorphic =...

Sufficient conditions for the law of the iterated logarithm for non-degenerate U-processes are presented. The law of the iterated logarithm for V-C subgraph classes of functions is obtained under second moment of the envelope. A bracketing condition for the law of the iterated logarithm for...

We establish zero-one laws for non-homogeneous forms of any finite order in Gaussian, non-Gaussian stable, or, more generally, in type G random variables. The random arguments in the form can be decoupled, totally coupled, or only partially coupled. These zero-one laws are applied to the study...

Assume that (Xi, Yi), 1 = i = n, are independent (p + 1)-variate vectors, where each Yi is at risk of being censored from the right and Xi is a vector of observable covariables. We introduce a (p + 1)-dimensional extension of the Kaplan-Meier estimator and show its consistency. Also a general...

Based on independent samples from several multivariate normal populations, possibly of different dimensions, the problem of simultaneous estimation of the mean vectors is considered assuming that the covariance matrices are unknown. Two loss functions, the sum of usual quadratic losses and the...

In this paper, we consider three different notions of positive dependence for a bivariate random vector: (i) total positivity of order 2, (ii) stochastic increasingness, and (iii) positive quadrant dependence. By defining three classes of arrangement-increasing functions, we show that these...

A smooth bootstrap method is used to find an estimator of the mean integrated squared error in density estimation. This provides a natural bootstrap selector for the bandwidth. Some rates of convergence and limit distributions are presented for this new selector as well as for some modification...

Künsch (1989, Ann. Statist.17 1217-1241) and Liu ane Singh (1992, in Exploring Limits of Bootstrap (R. Le Page and L. Billard, Eds.), pp. 225-248, Wiley, New York) have recently introduced a block resampling method that is successful in deriving consistent bootstrap estimates of distribution...

Sequential procedures are proposed to estimate the unknown mean vector of a multivariate linear process of the form Xt - [mu] = [summation operator][infinity]j = 0AjZt - j, where the Zt are i.i.d. (0, [Sigma]) with unknown covariance matrix [Sigma]. The proposed point estimation is...