Weak convergence and relative compactness of martingale processes with applications to some nonparametric statistics

Pranab Kumar Sen

Journal of Multivariate Analysis, 1972, vol. 2, issue 4, 345-361

Abstract: For forward and reverse martingale processes, weak convergence to appropriate stochastic (but, not necessarily, Wiener) processes is studied. In particular, it is shown that martingale processes are tight under a uniformly integrability condition, and also, convergence of finite dimensional distributions satisfying certain mild conditions implies the compactness of such processes. The theory is illustrated with the aid of a class of U-statistics and von Mises' differentiable statistical functions which need not be stationary of order zero. Weak convergence of the classical Cramér-von Mises goodness-of-fit statistic is also considered. The case of martingales with random indices is studied at the end.

Keywords: Martingales; reverse; martingales; and; sub-martingales; Weak; convergence; relative; compactness; U-statistics; and; von; Mises'; differentiable; statistical; functions (search for similar items in EconPapers)
Date: 1972
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