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 language | English |
|---|---|
| Pages (from-to) | 39-69 |
| Number of pages | 31 |
| Journal | American Journal of Mathematical and Management Sciences |
| Volume | 20 |
| Issue number | 1-2 |
| Publication status | Published - 2000 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - ML and REML estimation of Matusita's measure for two bivariate normal distributions with missing observations
AU - Minami, Mihoko
AU - Shimizu, Kunio
AU - Mishra, Satya N.
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
KW - Bias correction
KW - Niche overlap
KW - Similarity measures
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UR - http://www.scopus.com/inward/citedby.url?scp=0034540188&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0034540188
VL - 20
SP - 39
EP - 69
JO - American Journal of Mathematical and Management Sciences
JF - American Journal of Mathematical and Management Sciences
SN - 0196-6324
IS - 1-2
ER -