Estimation of similarity measure for multivariate normal distributions

Measures of niche overlap are used to assess the similarity or dissimilarity of two populations. Matusita's measure is one of commonly used niche overlap measures. We consider the problem of estimating Matusita's measure when samples are from multivariate normal distributions with unknown mean vectors and covariance matrices. Asymptotic variances and biases of Matusita's measure estimates are derived and bias reduction methods are proposed. Simulation results are shown to illustrate characteristics of the estimates and bias reduction methods.