ML and REML estimation of Matusita's measure for two bivariate normal distributions with missing observations

Mihoko Minami, Kunio Shimizu, Satya N. Mishra

Research output: Contribution to journalArticle

Abstract

The measures of niche overlap are used to assess the similarity or dissimilarity of two populations. Matusita's measure is one of the commonly used niche overlap measures. We discuss the problem of estimating Matusita's measure when the niches are bivariate normal distributions with missing observations. Under the assumption of equal variance of two variates in each population, we consider four cases depending on whether the variances and correlations for the two populations are common or different. The plug-in estimates of Matusita's measure by the Maximum Likelihood (ML) estimates and the REstricted or REsidual Maximum Likelihood (REML) estimates for dispersion parameters are considered, their asymptotic variances and bias are derived, and bias correction methods are proposed. Simulation study shows that the plug-in estimate by the REMLE tends to have smaller MSE than that by the MLE and the bias correction reduces MSE considerably.

Original languageEnglish
Pages (from-to)39-69
Number of pages31
JournalAmerican Journal of Mathematical and Management Sciences
Volume20
Issue number1-2
Publication statusPublished - 2000
Externally publishedYes

Fingerprint

Residual Maximum Likelihood
Bivariate Normal Distribution
Missing Observations
Maximum likelihood estimation
Normal distribution
Maximum Likelihood Estimation
Maximum likelihood
Maximum Likelihood
Niche
Bias Correction
Plug-in
Maximum Likelihood Estimate
Overlap
Dispersion Parameter
Restricted Maximum Likelihood
Asymptotic Bias
Asymptotic Variance
Dissimilarity
Estimate
Simulation Study

Keywords

  • Bias correction
  • Niche overlap
  • Similarity measures

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Applied Mathematics

Cite this

ML and REML estimation of Matusita's measure for two bivariate normal distributions with missing observations. / Minami, Mihoko; Shimizu, Kunio; Mishra, Satya N.

In: American Journal of Mathematical and Management Sciences, Vol. 20, No. 1-2, 2000, p. 39-69.

Research output: Contribution to journalArticle

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