Efficient semiparametric and parametric estimates are developed for a spatial autoregressive model, containing nonstochastic explanatory variables and innovations suspected to be non-normal. The main stress is on the case of distribution of unknown, nonparametric, form, where series...

We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series....

In this paper we introduce three natural ``score statistics" for testing the hypothesis that F(t_0)takes on a fixed value in the context of nonparametric inference with current status data. These three new test statistics have natural interpretations in terms of certain (weighted) L_2 distances,...

We studied the sharp large deviations for the log-likelihood ratio of an α-Brownian bridge. The full expansion of the tail probability for the log-likelihood ratio was obtained by using a change of measure.

A simple and effective method of assessing the reliability of a piece of software is to plot the cumulative number of failures observed during testing, N(x), against time x. Since no software is ever completely free of errors, be it careless minor oversights or the results of serious design...

In this paper we investigate the kernel estimator of the density for a stationary reversible Markov chain. The proofs are based on a new central limit theorem for a triangular array of reversible Markov chains obtained under conditions imposed to covariances, which has interest in itself.

Simple kernel-type estimators of integrals of general powers of general derivatives of probability densities are proposed. They are based on two simple properties, and in many circumstances enjoy optimal convergence rate.