Archive for William Strawderman

same risk, different estimators

Posted in Statistics with tags , , , , , on November 10, 2017 by xi'an

An interesting question on X validated reminded me of the epiphany I had some twenty years ago when reading a Annals of Statistics paper by Anirban Das Gupta and Bill Strawderman on shrinkage estimators, namely that some estimators shared the same risk function, meaning their integrated loss was the same for all values of the parameter. As indicated in this question, Stefan‘s instructor seems to believe that two estimators having the same risk function must be a.s. identical. Which is not true as exemplified by the James-Stein (1960) estimator with scale 2(p-2), which has constant risk p, just like the maximum likelihood estimator. I presume the confusion stemmed from the concept of completeness, where having a function with constant expectation under all values of the parameter implies that this function is constant. But, for loss functions, the concept does not apply since the loss depends both on the observation (that is complete in a Normal model) and on the parameter.

…and from Rutgers

Posted in Books, pictures, Statistics, Travel, University life, Wines with tags , , , , , on April 7, 2012 by xi'an

After my seminar in Princeton, I went to Rutgers University, in New Brunwick, New Jersey, to meet my friend Bill Strawderman and my former PhD student Aude Grelaud, and spent a pleasant evening with them. The next day, after a quick tour of the historical campus (great Old Dutch buildings!), I had a series of meetings with faculty members and with students, where we discussed extensions and applications of ABC. The seminar was on a tighter schedule than in Princeton, but we also managed to discuss the selection of summary statistics, while I insisted more on the (precision) gain brought by a reduction in the dimension of those summary statistics.

The schedule was tight as I had to catch a plane to Paris in New York (JFK) the same evening but taking advantage of the fairly efficient train facilities around New York, we still managed to share a quick beer at the Harvest Moon Brewery Café (I wish I had had time to get a tee-shirt from there!)… (The rest of the trip was 100% uneventful as I managed to sleep the whole flight back home!)

Festschrift for William E. Strawderman

Posted in Books, Statistics, Travel, University life, Wines with tags , , , , on March 19, 2012 by xi'an

Éric Marchand just sent me the news that the Festschrift volume he edited jointly with Dominique Fourdrinier and Andrew Rukhin in honour of our dear friend Bill Strawderman has now appeared on ProjectEuclid. It is freely accessible, thanks to this great IMS policy of making everything available on-line. As my research focus drifted away from shrinkage estimation and decision theory, I am sorry I could not contribute to the volume… (I “met” Bill through my readings during my PhD thesis and “in the flesh” when visiting Cornell two years later. He has produced some of the most elegant results in the area of Stein estimation, incl. the one that no proper Bayes estimator can be minimax in dimension four or less, and if a particular shrinkage estimator was to be “Hall-of-Fame-d”, it would be his! Bill visited us in Rouen (Dominique and I) many times and even learned French in order to teach there. I also happened to have the most hilarious moment of my life [so far!] with him and George Casella on an Ithaca country road, late on a summer night, but I cannot alas disclose the details!!!)