Advertisement

Convergence in Distribution in Metric Spaces

  • David Pollard
Part of the Springer Series in Statistics book series (SSS)

Abstract

We write a statistic as a functional on the sample paths of a stochastic process in order to break an analysis of the statistic into two parts: the study of continuity properties of the functional; the study of the stochastic process as a random element of a space of functions. The method has its greatest appeal when many different statistics can be written as functionals on the same process, or when the process has a form that suggests a simple approximation, as in the goodness-of-fit example from Chapter I. There we expressed various statistics as functionals on the empirical process U n , which defines a random element of D[0, 1]. Doob’s heuristic argument suggested that U n should behave like a brownian bridge, in some distributional sense.

Keywords

Weak Convergence Representation Theorem Regular Point Random Element Closed Ball 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • David Pollard
    • 1
  1. 1.Department of StatisticsYale UniversityNew HavenUSA

Personalised recommendations