We obtain limit theorems for likelihood ratio and cumulative sums tests. In the case of the likelihood ratio the centralising and normalising sequences go to infinity and the limit is the Gumbel (double exponential) distribution. The first and the last few observations determine the limit, which...

Under the random censorship model from the right, we construct confidence bands for the (1 - p) percentile residual lifetime, R(p)(t) = Q(1 - p(1 - F0(t))) - t, where F0 and Q denote the distribution and quantile functions, respectively. We first prove that the scaled PL(1 - p) percentile...

Very sparse contingency tables with a multiplicative structure are studied. The number of unspecified parameters and the number of cells are growing with the number of observations. Consistency and asymptotic normality of natural estimators are established. Also uniform convergence of the...

This paper considers the problem of estimating the coefficient matrix B: m - p in a normal multivariate regression model under the risk matrix : m - m and obtains classes of minimax estimators for Baranchik type, Strawderman type, Efron-Morris type, and Stein type estimators.

Let (X, Y), (X1, Y1), ..., (Xn, Yn) be i.d.d. Rr - R-valued random vectors with EY [infinity], and let Qn(x) be a kernel estimate of the regression function Q(x) = E(YX = x). In this paper, we establish an exponential bound of the mean deviation between Qn(x) and Q(x) given the training sample...

In Campbell (1982, IMS Lecture Notes--Monograph Series Vol. 2, pp. 243-256, IMS, Hayward, CA) and Campbell and Földes (1982, Proceedings, Internat. Colloq. Nonparametric Statist. Inform., 1980, North-Holland, New York) some asymptotic properties of bivariate empirical hazard processes under...

Let [theta]n(x) be an estimator of a smooth function [theta](x). It is proved that [theta](x) can be estimated easier than its derivative [theta](s)(x), providing for [theta]n(s) - [theta](s)q an upper bound that depends on [theta]n - [theta]q. The same bound can be used as a tool to derive...

This paper addresses the representation of continuous-time strongly harmonizable periodically correlated processes and their covariance functions. We show that the support of the 2-dimensional spectral measure is constrained to a set of equally spaced lines parallel to the diagonal. Our main...

In a standard linear model, we explore the optimality of the least squares estimator under assuptions stronger than those for the Gauss-Markov theorem. The conclusion is then much stronger than that of the Gauss-Markov theorem. Specifically, two results are cited below: Under the assumption that...

Necessary and sufficient conditions for weak convergence and strong (functional) limit theorems for the negative parts of weighted multivariate empirical processes are obtained. These results are considerably different from those for the positive parts (or absolute values) of these processes....