We consider a class of discrete parameter Markov processes on a complete separable metric space S arising from successive compositions of i.i.d. random maps on S into itself, the compositions becoming contractions eventually. A sufficient condition for ergodicity is found, extending a result of...

Autoregressive models are important in describing the behaviour of the observed time series. One of the reasons is that a covariance stationary process can be approximated by an autoregressive model. Thus, e.g., the spectrum of a covariance stationary time series can be approximated by the...

Barndorff-Nielsen's formula (normed likelihood with constant-information metric) has been proffered as an approximate conditional distribution for the maximum-likelihood estimate, based on likelihood functions. Asymptotic justifications are available and the formula coincides with the...

We consider the problem of estimation of [mu]1 when it is suspected that [mu]1 [approximate] [mu]2 based on independent samples from Np([mu]1, [sigma]2V1) and Np([mu]2, [sigma]2V2). We assume V1, V2 known but [sigma]2 unknown. First, the EB estimator is derived and its Bayesian and frequentist...

Let (T1, T2) be a non-negative random vector which is subjected to censoring random intervals [X1, Y1] and [X2, Y2]. The censoring mechanism is such that the available informations on T1 and T2 are expressed by a pair of random vectors W=(W1, W2) and [delta]=([delta]1, [delta]2), where...

Strong limit theorems are obtained for maximal and minimal multivariate kn-spacings, where {kn}n=1[infinity] is a sequence of positive integers satisfying kn = 0(log n). The shapes, in terms of which these spacings are defined, are allowed to be quite general. They must only satisfy certain...

In a k (=2) sample model, isotonic estimators of locations [theta]1, ..., [theta]k take into consideration the prior restraint that [theta]1 = ... = [theta]k. Though these estimators are appealling, they are generally biased. The union-intersection (UI-) principle and the theory of M-estimation...

Given a generalized Gaussian random field on a domain D in Rd, we are interested in a restriction of the parameter to a lower dimensional submanifold and discuss the variation when the manifold varies.

Starting from recent strong and weak approximations to the partial sums of i.i.d. random vectors (cf. U. Einmahl, Ann. Probab., 15 1419-1440), some corresponding invariance principles are developed for associated renewal processes and random sums. Optimality of the approximation is proved in the...