Maximum Likelihood Estimation in Small Incomplete Samples from the Bivariate Normal Distribution

D. A. Ratkowsky

Journal of the Royal Statistical Society Series C, 1974, vol. 23, issue 2, 180-189

Abstract: Maximum likelihood estimation of the parameters of a bivariate normal distribution using incomplete samples has been studied, special attention being paid to small data sets. A comparison of the asymptotic variance–covariance matrix relevant to such incomplete sets of data with the matrix obtained from maximum likelihood estimation in the case where all data sets are complete enables one to deduce an effective sample size for the estimation of each parameter. Using these effective sample sizes the results of a simulation study indicate that each estimator possesses properties similar to the corresponding estimator from the complete data case, except that in some simulations there are significant departures of the higher sample moments from the expected values. The results imply that the asymptotic formulae for the variances of the estimators are good approximations in small samples.

Date: 1974
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