Sequential risk-efficient estimation for the ratio of two binomial proportions

A risk-efficient sequential point estimator is considered for the ratio of two independent binomial proportions based on maximum likelihood estimation under squared error loss and cost proportional to the observations. It is assumed that the cost per observation is constant. First-order asymptotic expansions are obtained for large-sample properties of the proposed procedure. Performance of the procedure is studied through the criteria of risk efficiency and regret analysis. Monte Carlo simulation is carried out to obtain the expected sample size that minimizes the risk and to examine its finite sample behavior. An example is provided to illustrate its use.