Bias correction for segregation ratio estimation in human genetics

Segregation ratio estimation has long been important in human genetics. A s imple truncated binomial model is considered that assumes complete ascertai nment and a deterministic genotype-phenotype relationship. A simple but int uitively appealing estimator of the segregation ratio, previously proposed, is shown to have a negative bias. It is also shown that the bias of this e stimator can be largely reduced via a randomization device, resulting in a new estimator that has the same large-sample behavior but with a negligible bias (decaying at a geometric rate). Numerical results are given to show t he small-sample performance of this new estimator. An extension to incomple te ascertainment is also considered.