Stat Colloquium: Dr. Nitis Mukhopadhyay

Title: A General Sequential Fixed-Accuracy Confidence Interval Methodology for a Positive Parameter

Abstract: Estimation of positive parameters is important in a number of areas including ecology, biology, medicine, nuclear power, and study of cell membranes. We developed a fixed-accuracy sequential confidence interval methodology for the mean of a negative binomial (NB) distribution having its thatch parameter unknown with applications in statistical ecology. In this presentation, we outline a broad structure for fixed-accuracy sequential confidence interval estimation methodology for a positive parameter of an arbitrary distribution which may be discrete or continuous. We construct a confidence interval of the form: [T/d, dT] with d > 1, based on a maximum likelihood (ML) estimator T. We show attractive properties such as (i) asymptotic (as d↓1) consistency and (ii) asymptotic first-order efficiency.

We emphasize illustrations corresponding to the Bernoulli distribution (odds-ratio of poisonous mushrooms), Poisson distribution (radioactive decay of isotopes), and a normal distribution with the same mean and variance (real-time 911 calls dispatch). Data analyses from large-scale simulations are briefly incorporated to highlight encouraging performances of the proposed methodology. Some material comes from joint research with Swarnali Banerjee (Associate Professor & Director of Data Science, Department of Mathematics & Statistics, Loyola University-Chicago), a former Ph.D. student of mine