Statistical experiments possess the property of adaptivity, if the ignorance of a nuisance parameter does not cause any loss in efficiency. In order to include a large variety of cases, the efficiency is measured in terms of minimax bounds. It is shown that a necessary and sufficient condition...

The information given by the position of the Brownian sheet along or near a curve can be represented by the sharp field, the minimal splitting field, or the germ field. When the curve is a separation line, we show that the last two fields are always equal and give necessary and sufficient...

We construct a simple algorithm, based on Newton's method, which permits asymptotic minimization of L1 distance for nonparametric density estimators. The technique is applicable to multivariate kernel estimators, multivariate histogram estimators, and smoothed histogram estimators such as...

Given a weakly converging sequence of measures, we study the convergence of the corresponding integrals of a continuous unbounded multifunction. We also study the implication of these results to variational problems, and provide further approximating results for the integral of a multifunction,...

In this note we development the relation between another type of conditional convergence of a sequence of random variable (r.v.). Moreover, we generalise the theorem of convergence in L1 for amarts.

Necessary and sufficient conditions are established for the set of all admissible linear estimators under M0 to be contained in the corresponding set of estimators under M, where M0 and M are general Gauss-Markov models with identical model matrices but different dispersion matrices. As...

In this paper strong consistency and uniform complete consistency of the nonparametric density estimator proposed by [5], 1049-1051) is proved for [phi]-mixing and [alpha]-mixing processes.

Let X = (X1,...,Xp)t to be an observation from a p-variate normal distribution with unknown mean vector [theta] = ([theta]1,...,[theta]p)t and known covariance matrix [Sigma]. It is desired to estimate [theta] under the quadratic loss L([theta], [delta]) = ([theta] - [delta])tQ([theta] -...

We study the asymptotic behaviour of U-statistics type processes which can be used for detecting a changepoint of a random sequence. Invariance principles are proved for these processes.

Let {Xt} be a Gaussian ARMA process with spectral density f[theta]([lambda]), where [theta] is an unknown parameter. The problem considered is that of testing a simple hypothesis H:[theta] = [theta]0 against the alternative A:[theta] [not equal to] [theta]0. For this problem we propose a class...