Is There Any Magic Left in Statistical Inference and Probability?

Nitis Mukhopadhyay
Department of Statistics
University of Connecticut-Storrs

ABSTRACT:
I will emphasize that mathematical statistics has not lost its importance or relevance today just because of the upsurge of recent thrust in methodological research and fast statistical computing. I do not accept any line drawn to separate methodological research and statistical computing from basic research. One depends on the others. I am convinced that mathematical statistics is a living and breathing thing. Contrary to the beliefs of many around, it is not dead. It has never been and never will it be dead. One can surely continue to publish intriguing papers in mathematical statistics if one is trained and willing. Personally, I find that going back to the basic concepts that have been around from the days of Fisher-Neyman-Pearson-Rao-Blackwell plus host of others and questioning them critically can be very fruitful and satisfying. I have written a few papers arising from some such critical-curiosity-seeking adventures. I will share my enthusiasm with examples from topics and concepts such as covariances, correlations, independence, marginals, multivariate distributions, MVUEs, invariance, and UMPI tests. I will try my best to get into as many topics as possible without showing many details.