Estimators for functions of the probability of success in a sequence of bernoulli trials

Abstract

Suppose that a sample of N experimental subjects are ran-daaly selected from a population of potential subjects. Sacs,sequence of T independent Bernoulli trials. The summary data from this experiment consists of the number of successes out of T trials attained by each of the N subjects. Each subject say be characterized by his probability p of success on a Bernoulli trial. This probability remains constant over successive trials,. but varies from subject to subject. Let g be a continuous function defined over the interval zero to one., Then, g(p) is a random variable over the population of potential subjects. It is desired to utilise the summary data from the experiment to estimate to- both the sample mean and the population mean of g(p).Two estimation procedures are proposed: a general method and an alternative method for use only with large N. The first method Minimizes the maximum possible mean square error. The second method consists of approximating the function g with a polynomial and, then, constru...