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
DOIs
Publication statusPublished - 2000 Jan 1
Externally publishedYes

Keywords

  • Bias correction
  • Niche overlap
  • Similarity measures

ASJC Scopus subject areas

  • Business, Management and Accounting(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'ML and REML estimation of matusita’s measure for two bivariate normal distributions with missing observations'. Together they form a unique fingerprint.

  • Cite this