A conversation with Lucien Le Cam

Abstract

Lucien Le Cam is currently Emeritus Professor of Mathematics and Statistics at the University of California, Berkeley. He was born on November 18, 1924, in Croze, Creuse, France. He received a Licence es Sciences from the University of Paris in 1945, and a Ph.D. in Statistics from the University of California at Berkeley in 1952. He has been on the faculty of the Statistics Department at Berkeley since 1952 except for a year in Montreal, Canada, as the Director of the Centre de Recherches Mathématiques (1972--1973). He served as Chairman of the Department of Statistics at Berkeley (1961–1965) and was co­editor with J. Neyman of the Berkeley Symposia.

Professor Le Cam is the principal architect of the modern asymptotic theory of statistics and has also made numerous other contributions. He developed a mathematical system that substantially extended Wald's statistical decision theory to the version being used today. With his introduction of the distance between experiments, we now have a coherent statistical theory that links the asymptotics and the statistical decision theory. Encompassed in the theory are the concepts of contiguity, asymptotic sufficiency, a new method of constructing estimators (the one­step estimator), the theory of local asymptotic normality (LAN), metric dimension and numerous other seminal ideas. The metric dimension, introduced in 1973, has been found to be fundamentally important in studying nonparametric or semiparametric problems. This monumental work culminated in a big book, Asymptotic Methods in Statistical Decision Theory, published by Springer in 1986.

Professor Le Cam's scientific contributions are not limited to theoretical statistics. At age 23 he introduced the characteristic functional technique (after Kolmogorov, but independently) to study the spatial and temporal distribution of rainfall and its relation to stream flow. It resulted in a model known as Le Cam’s model in hydrology. In the domain of probability theory, he was one of the early contributors to the study of convergence of measures in topological spaces. He refined the approximation theorems and the concentration inequalities of Kolmogorov and made extensions of these results to infinite­dimensional spaces. We also owe to him the introduction of the concepts of $\tau$-smooth, and $\sigma$­smooth that are widely used today.

In honor of his 70th birthday in 1994, a week­long workshop and a conference were held at Yale University, organized by Professor David Pollard. In addition, a Festschrift for Le Cam, Research Papers in Probability and Statistics Papers, was published by Springer in 1997. He is married to Louise Romig, the daughter of a founder of statistical quality control, Harry Romig. They have three grown children, Denis, Steven and Linda.