Nonparametric composite hypothesis testing in an asymptotic regime

Qunwei Li, Tiexing Wang, Donald J. Bucci, Yingbin Liang, Biao Chen, Pramod K. Varshney

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypothesis grow exponentially large. Such asymptotic analysis is important in many practical problems, where the number of variations that can exist within a family of distributions can be countably infinite. We introduce the notion of discrimination capacity, which captures the largest exponential growth rate of the number of hypothesis relative to the sample size so that there exists a test with asymptotically vanishing probability of error. Our approach is based on various distributional distance metrics in order to incorporate the generative model of the data. We provide analyses of the error exponent using the maximum mean discrepancy and Kolmogorov-Smirnov distance and characterize the corresponding discrimination rates, i.e., lower bounds on the discrimination capacity, for these tests. Finally, an upper bound on the discrimination capacity based on Fano's inequality is developed. Numerical results are presented to validate the theoretical results.

Original languageEnglish (US)
Article number8438996
Pages (from-to)1005-1014
Number of pages10
JournalIEEE Journal on Selected Topics in Signal Processing
Volume12
Issue number5
DOIs
StatePublished - Oct 2018

Keywords

  • Channel coding
  • Kolmogorov-Smirnov distance
  • discrimination rate
  • error exponent
  • maximum mean discrepancy

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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