A note on estimation using self-contained subsets

In a recent article, Li (1986, Annals of Human Genetics 50, 259-270) described a method of subdividing genetic data into self-contained subsets for estimating parameters of interest. The method was illustrated for binomial, multinomial, and Poisson distributions. In the case of the Poisson distribution, Li's estimate is always larger than the sample mean and the reason for this is discussed. It is pointed out that the method based on self-contained subsets gives unbiased estimates for binomial and multinomial parameters, but that the estimate of the Poisson parameter is biased unless all available subsets are included in the estimation.