Rubin was considered a
polymath with a unique ability to solve complex problems. He was a prolific researcher, publishing over 130 papers that have become standard texts in various fields. His key contributions include: •
Multivariate Analysis: He co-authored seminal papers with
T.W. Anderson on the distribution theory of
maximum likelihood estimators in
factor analysis and
structural equation models. •
Monotone likelihood ratio: He is credited with the widely used and fundamental concept of monotone likelihood ratio families. •
Bayesian Inference: Rubin was a lifelong
Bayesian statistician who took the theory and axioms of
Leonard Jimmie Savage literally, and he contributed significantly to the theory of
Bayes risks. •
Econometrics: He worked on problems related to the
simultaneous equations model in economics, including the development of the
Limited information maximum likelihood (LIML) estimator. •
Set Theory and Probability: His work also included contributions to set theory, the
theory of moderate deviations, and the characterization of probability distributions. •
Hypothesis testing: in collaboration with
Samuel Karlin, the
Karlin-Rubin theorem provides a method for finding uniformly most powerful tests for one-sided hypotheses, a significant contribution to the theory of hypothesis testing. He was an inaugural Fellow of the
American Mathematical Society and a Fellow of the
Institute of Mathematical Statistics. ==Family==