Sequential Shrinkage U - Statistics : General Asymptotics

Degenerate U- and V -statistics under ergodicity: Asymptotics, bootstrap and applications in statistics

We derive the asymptotic distributions of degenerate U and V -statistics of stationary and ergodic random variables. Statistics of these types naturally appear as approximations of test statistics. Since the limit variables are of complicated structure, quantiles can hardly be obtained directly. Therefore, we prove a general result on the consistency of model-based bootstrap methods for U and V...

Decomposability of high-dimensional diversity measures: Quasi-U-statistics, martingales and nonstandard asymptotics

In complex diversity analysis, specially arising in genetics, genomics, ecology and other high-dimensional (and sometimes low sample size) data models, typically subgroup-decomposability (analogous to ANOVA decomposability) arises. In groupdivergence of diversity measures in a high-dimension low sample size scenario, it is shown that Hamming distance-type statistics lead to a general class of q...

Ghosh ’ s contribution to statistics : A brief outline

Professor Jayanta Kumar Ghosh has contributed massively to various areas of Statistics over the last five decades. Here, we survey some of his most important contributions. In roughly chronological order, we discuss his major results in the areas of sequential analysis, foundations, asymptotics, and Bayesian inference. It is seen that he progressed from thinking about data points, to thinking a...

Asymptotics for the Moment Convergence of U-Statistics in LIL

3 Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlevé Equation . I

The degenerate third Painlevé equation, u= (u ) u −u′ τ + τ (−8εu2+2ab)+b2 u , where ε, b∈R, and a∈C, and the associated tau-function are studied via the Isomonodromy Deformation Method. Connection formulae for asymptotics of the general as τ→±0 and ±i0 solution and general regular as τ→±∞ and ±i∞ solution are obtained. 2000 Mathematics Subject Classification. 33E17, 34M40, 34M50, 34M55, 34M60 ...