Measure-transformed quasi likelihood ratio test

Koby Todros, Alfred O. Hero

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations

Abstract

In this paper, a generalization of the Gaussian quasi likelihood ratio test (GQLRT) for simple hypotheses is developed. The proposed generalization, called measure-transformed GQLRT (MT-GQLRT), selects a Gaussian probability model that best empirically fits a transformed probability measure of the data. By judicious choice of the transform we show that, unlike the GQLRT, the proposed test can gain sensitivity to higher-order statistical moments and resilience to outliers leading to significant mitigation of the model mismatch effect on the decision performance. Under some mild regularity conditions we show that the proposed test statistic is asymptotically normal. A data driven procedure for optimal selection of the measure transformation parameters is developed that maximizes an empirical estimate of the asymptotic power given a fixed empirical asymptotic size. The MT-GQLRT is applied to signal classification in a simulation example that illustrates its sensitivity to higher-order statistical moments and resilience to outliers.

Original languageEnglish
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4259-4263
Number of pages5
ISBN (Electronic)9781479999880
DOIs
StatePublished - 18 May 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: 20 Mar 201625 Mar 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Conference

Conference41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Country/TerritoryChina
CityShanghai
Period20/03/1625/03/16

Keywords

  • Higher-order statistics
  • hypothesis testing
  • probability measure transform
  • robust statistics
  • signal classification

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