Minimum Hellinger Distance Estimation of Mixture Proportions

Abstract

Beran (1977) showed that, under certain restrictive conditions, the minimum distance estimator based on the Hellinger distance (MHDE) between a projection model density and a nonparametric sample density is an exception to the usual perception that a robust estimator cannot achieve full efficiency under the true model. We examine the MHDE in the case of estimation of the mixing proportion in the mixture of two normals. We discuss the practical feasibility of employing the MHDE in this setting and examine empirically its robustness properties. Our results indicate that the MHDE obtains full efficiency at the true model while performing comparably with the minimum distance estimator based on Cramer-von Mises distance under the symmetric departures from component normality considered.

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Document Details

Document Type
Technical Report
Publication Date
Jun 11, 1990
Accession Number
ADA223536

Entities

People

  • Paul W. Eslinger
  • Paul Whitney
  • Wayne A. Woodward

Organizations

  • Southern Methodist University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Bandwidth
  • Computations
  • Data Analysis
  • Data Mining
  • Data Science
  • Distribution Functions
  • Estimators
  • Information Science
  • Normal Distribution
  • Normality
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Algorithms
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Statistical inference.