Yakov Nikitin

Large deviations of U-empirical Kolmogorov–Smirnov tests and their efficiency

Non-degenerate U-empirical Kolmogorov–Smirnov tests are studied and their large deviation asymptotics under the null-hypothesis is described. Several examples of such statistics used for testing goodness-of-fit and symmetry are considered. It is shown how to calculate their local Bahadur efficiency.

Tail behavior of anisotropic norms for Gaussian random fields

We investigate the logarithmic large deviation asymptotics for anisotropic norms of Gaussian random functions of two variables. The problem is solved by the evaluation of the anisotropic norms of corresponding integral covariance operators. We find the exact values of such norms for some important classes of Gaussian fields. To cite this article: M. Lifshits et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Approximate asymptotic Bahadur efficiency of independence tests with random sample size

We compare various kind of independence tests based on samples with random size, in order to provide practitioners with some guidance for their choice based on approximate Bahadur efficiency. Such results are obtained for a wide class of distributions of the random index; the efficiency slopes of the statistics we consider are then expressed in terms of the parameters of these same distributions.