Current Research and Scholarly Interests
Lai is widely recognized as a prolific leader in the field of sequential statistical analysis. Among his principal achievements is the development of a comprehensive theory of sequential tests of composite hypotheses, unifying previous approaches and providing far-reaching extensions to cope with the practical complexities that arise in the applications to group sequential clinical trials. In particular, this theory paved the way for his ground-breaking work with Shih on flexible and nearly-optimal group sequential tests that can self-tune to the unknown parameters during the course of the trial, under pre-specified constraints on the maximum sample size and significance level.
Other major breakthroughs include (a) accurate confidence intervals following sequential tests by using an innovative resampling approach, (b) a definitive solution to the long-standing multi-armed bandit problem, and (c) the development of statistically and computationally efficient sequential change-point detection procedures in multivariate time series and stochastic systems, for applications to industrial quality control, fault detection in engineering systems and segmentation in computational biology.
Besides sequential analysis, Lai has also made ground-breaking contributions to (i) stochastic approximation and recursive estimation, (ii) adaptive control of linear stochastic systems and Markov decision processes, (iii) saddlepoint approximations and boundary-crossing probabilities in Markov random walks and random fields, and (iv) survival analysis, in particular, rand- and M-estimators in regression models when the response variable is subject to censoring and truncation, and interim analysis of clinical trials with failure-time endpoints.