Fixed-width confidence interval based on a minimum Hellinger distance estimator

In the context of discrete data, a sequential fixed-width confidence interval for an unknown parameter in a parametric model is constructed using a minimum Hellinger distance estimator (MHD) as the center of the interval. It is shown that our sequential procedure is asymptotically consistent and efficient, when the assumed parametric model is correct. These results, in addition to being exactly same as those obtained by Khan [1969, A general method of determining fixed-width confidence intervals. Ann. Math. Statist. 40, 704–709] and Yu [1989, On fixed-width confidence intervals associated with maximum likelihood estimation. J. Theoret. Probab. 2, 193–199] using a maximum likelihood estimator (MLE), offer an alternative which has several in-built robustness properties. Monte Carlo simulations show that the performance of our sequential procedure based on MHD, measured in terms of average sample size and the coverage probability, are as good as those based on MLE, when the assumed Poisson model is correct. However, when the samples come from a gross-error contaminated Poisson model, our numerical results show that the deviation from the Poisson model assumption severely affects the performance of the sequential procedure based on MLE, while the procedure based on MHD continues to perform well, thus exhibiting robustness of MHD against gross-error contaminations even for random sample sizes.