ON THE ASYMPTOTIC NORMALITY OF MULTINOMIAL POPULATION SIZE ESTIMATORS WITH APPLICATION TO BACKCALCULATION OF AIDS EPIDEMIC

摘要

Estimation of the unknown size of a multinomial distribution is required in some important applications. It has been previously shown that the maximum likelihood estimators of the size and other parameters in the multinomial distribution are asymptotically normal under suitable regularity conditions. Unfortunately, one of these conditions is difficult to verify in practice. Here we present an alternative regularity condition that is straightforwardly verifiable. An application to the backcalculation estimates of AIDS incidence is presented. Explicit formulae are given for the asymptotic variances and covariances of the backcalculation estimators. The associated confidence interval for the size of the HIV infected population is comparable to the likelihood-ratio-test-based interval given in Brookmeyer & Gall (1988). A simulation study shows that the asymptotic normal interval is highly accurate in terms of coverage probability.