Erich Lehmann 20 November 1917 – 12 September 2009
Memory Lane 1 Year (with update): Today is Erich Lehmann’s birthday. The last time I saw him was at the Second Lehmann conference in 2004, at which I organized a session on philosophical foundations of statistics (including David Freedman and D.R. Cox).
I got to know Lehmann, Neyman’s first student, in 1997. One day, I received a bulging, six-page, handwritten letter from him in tiny, extremely neat scrawl (and many more after that). He told me he was sitting in a very large room at an ASA meeting where they were shutting down the conference book display (or maybe they were setting it up), and on a very long, dark table sat just one book, all alone, shiny red. He said he wondered if it might be of interest to him! So he walked up to it…. It turned out to be my Error and the Growth of Experimental Knowledge (1996, Chicago), which he reviewed soon after. Some related posts on Lehmann’s letter are here and here.
That same year I remember having a last-minute phone call with Erich to ask how best to respond to a “funny Bayesian example” raised by Colin Howson. It is essentially the case of Mary’s positive result for a disease, where Mary is selected randomly from a population where the disease is very rare. See for example here. (It’s just like the case of our high school student Isaac). His recommendations were extremely illuminating, and with them he sent me a poem he’d written (which you can read in my published response here*). Aside from being a leading statistician, Erich had a (serious) literary bent.
Juliet Shafer, Erich Lehmann, D. Mayo
The picture on the right was taken in 2003 (by A. Spanos).
(2014 update): It was at this meeting that I proposed organizing a session for the 2004 Erich Lehmann Conference that would focus on “Philosophy of Statistics”. He encouraged me to do so. I invited David Freedman (who accepted), and then had the wild idea of inviting Sir David Cox. He too accepted! (Cox and I later combined our contributions into Mayo and Cox 2006).
Mayo, D. G (1997a), “Response to Howson and Laudan,” Philosophy of Science 64: 323-333.
Mayo, D.G. and Cox, D. R. (2006) “Frequentists Statistics as a Theory of Inductive Inference,” Optimality: The Second Erich L. Lehmann Symposium (ed. J. Rojo), Lecture Notes-Monograph series, Institute of Mathematical Statistics (IMS), Vol. 49: 77-97.
(Selected) Books by Lehmann)
- Testing Statistical Hypotheses, 1959
- Basic Concepts of Probability and Statistics, 1964, co-author J. L. Hodges
- Elements of Finite Probability, 1965, co-author J. L. Hodges
- Lehmann, Erich L.; With the special assistance of H. J. M. D’Abrera (2006). Nonparametrics: Statistical methods based on ranks (Reprinting of 1988 revision of 1975 Holden-Day ed.). New York: Springer. pp. xvi+463. ISBN 978-0-387-35212-1. MR 2279708.
- Theory of Point Estimation, 1983
- Elements of Large-Sample Theory (1988). New York: Springer Verlag.
- Reminiscences of a Statistician, 2007, ISBN 978-0-387-71596-4
- Fisher, Neyman, and the Creation of Classical Statistics, 2011, ISBN 978-1-4419-9499-8 [published posthumously]
Articles (3 of very many)
- Lehmann, E.L.; Scheffé, H. (1950). “Completeness, similar regions, and unbiased estimation. I.”. Sankhyā: the Indian Journal of Statistics 10 (4): 305–340. JSTOR 25048038. MR 39201.
- Lehmann, E.L.; Scheffé, H. (1955). “Completeness, similar regions, and unbiased estimation. II”. Sankhyā: the Indian Journal of Statistics 15 (3): 219–236. JSTOR 25048243. MR 72410.
- Lehmann, E. L. 1993. “The Fisher, Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?” Journal of the American Statistical Association 88 (424): 1242–1249.
Error Statistics Philosophy 