Interval Estimation of the Overlapping Coefficient of Two Multivariate Normal Distributions

This paper introduces the use of a generalized pivotal statistic for the interval estimation of the overlapping coefficient between two multivariate normal distributions. Percentile bootstrap and the delta methods are also considered. Simulation results are reported to compare the performance of these methods in terms of expected lengths and coverage probabilities of the confidence intervals. The value of overlapping coefficient is the major deciding factor affecting the performance of the confidence intervals. For small values of rho, the generalized pivotal quantity (GPQ) method provides satisfactory performance. Illustrative examples are also presented.