Nonparametric Composite Hypothesis Testing in an Asymptotic Regime

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

Research output: Contribution to journalArticle

1 Scopus citations


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 hypotheses 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 hypotheses 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 (MMD) and Kolmogorov-Smirnov (KS) 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)
JournalIEEE Journal on Selected Topics in Signal Processing
StateAccepted/In press - Aug 16 2018


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

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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