An Invariance Property of the Generalized Likelihood Ratio Test

Abstract

The generalized likelihood ratio test (GLRT) is invariant with respect to transformations for which the hypothesis testing problem itself is invariant. This result from the statistics literature is presented in the context of some simple signal models. This is an important property of the GLRT in light of its widespread use and the recent interest in invariant tests applied to signal processing applications. The GLRT is derived for some examples in which the uniformly most powerful invariant (UMPI) test does and does not exist, including one in which the UMPI test exists and is not given by the GLRT.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2003
Accession Number
ADA525833

Entities

People

  • Joseph R. Gabriel
  • Stephen M. Kay

Organizations

  • Naval Undersea Warfare Center

Tags

DTIC Thesaurus Topics

  • Data Science
  • Delta Functions
  • Detection
  • Detectors
  • Electrical Engineering
  • Electronic Mail
  • Engineering
  • False Alarms
  • Gaussian Noise
  • Information Operations
  • Invariance
  • Noise
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Signal Processing

Fields of Study

  • Mathematics

Readers

  • Plasma Physics / Magnetohydrodynamics
  • Radar Systems Engineering.
  • Regression Analysis.