### 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 |

### Fingerprint

### Keywords

- Bias correction
- Niche overlap
- Similarity measures

### ASJC Scopus subject areas

- Industrial and Manufacturing Engineering
- Applied Mathematics

### Cite this

*American Journal of Mathematical and Management Sciences*,

*20*(1-2), 39-69.

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

Research output: Contribution to journal › Article

*American Journal of Mathematical and Management Sciences*, vol. 20, no. 1-2, pp. 39-69.

}

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

UR - http://www.scopus.com/inward/record.url?scp=0034540188&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034540188&partnerID=8YFLogxK

M3 - Article

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 -