Abstract: A martingale estimating function is proposed to estimate the number of species under a multinomial model with possibly unequal cell probabilities. This approach provides a class of estimators including the maximum likelihood estimator for the equiprobable case and the nonparametric sample coverage estimator (Chao and Lee (1992)) for the non-equiprobable case. Consistency of the proposed estimators is discussed. A simulation study investigates the behavior of the proposed procedure. A data set on Chinese poems is given for illustration.
Key words and phrases: Number of classes, multinomial, heterogeneity, sample coverage, zero mean martingale.