Talk:Piet Groeneboom

relevancy

It is mentioned that Piet Groeneboom studied medicine and psychology and did the "candidate exam" (a type of exam that does not exist anymore, but was a bit more than a bachelor now) in psychology. I do not think this is very relevant and that it could be omitted. One could mention that he did his masters in Mathematics cum laude, but I do not know whether that is very relevant either. Below I will describe some aspects of his work that seem more relevant.

1. Sanov's theorem. Piet Groeneboom proved for the first time Sanov's theorem in a Mathematical Centre report: https://ir.cwi.nl/pub/8069 in 1976 in full generality, using the tau topology. The tau topology is a topology "between" the topology of total variation and the topology of weak convergence. It is the topology of convergence on all Borel sets, but not uniform convergence, as in the topology of total variation. The tau topology is not metrizable. Sanov's theorem is a special case of Lemma 1.3.1 in his dissertation "Large deviations and asymptotic efficiencies (1979), reprinted as Mathematical Centre Tract in 1980.

2. Central limit theorem for convex hulls. Piet Groeneboom proved for the first time a central limit theorem for the number of vertices of the convex hull of a uniform sample of points in the interior of a convex polygon: Groeneboom, Piet. Limit theorems for convex hulls. Probab. Theory Related Fields 79 (1988), no. 3, 327--368. MR0959514. Later Nagaev and Khamdamov extended this result to a theorem for the joint distribution of the area and the number of points in a Tashkent preprint (1991). Later summaries of this work are given in Groeneboom, Convex Hulls of Uniform Samples from a Convex polygon (2012) (with a new proof of the result of Nagaev and Khamdamov),https://www.jstor.org/stable/41714053, in Adv. Appl. Probability, and Chapter 12, written by Rolf Schneider in "Handbook of Discrete and Computational Geometry” (3rd edition) van Goodman, O'Rourke en Toth, (2017). Rolf Schneider says: "The first central limit theorems for random variables φ(K, n) (= the number of vertices of the convex hull) were obtained in pioneering work of Groeneboom". See also the book "Stochastic and Integral Geometry", Rolf Schneider and Wolfgang Weil, Springer 2008.

3. Characterization of nonparametric estimators of a convex funtion/density and its convergence to the "invelope" of integrated Brownian motion + the 4th power of the time variable: "Estimation of a Convex Function: Characterizations and Asymptotic Theory" Annals of Statistics (2001), and "A canonical process for estimation of convex functions: the invelope of integrated Brownian motion +t^4",", Annals of Statistics (2001). Co-authors: Geurt Jongbloed and Jon Wellner.

4. When at MSRI, Berkeley, in 1983, he proved that the method Perlman and Olkin suggest to prove a monotonicity property of a multivariate test statistic i their paper in the Annals of Ststistics 8, 1326-1341 (1980), will never work, because the required total positivity property (TP_2) does not hold. This was published in Indagationes Mathematicae (2000): A monotonicity property of the power of multivariate tests, Indag. Mathem, 11 (2), 209-218, with co-author Donald R. Truax.

5. Book with Jon Wellner (1992). The second part of this book consisted of lectures, given at the summer course on Advanced Probability, Stanford University, 1990. It is still available as Technical Report 378, Juli 1991, Stanford University.

6. Affiliations: apart from what is mentioned, Piet Groeneboom was temporarily affiliated with Stanford University and Université Paris 6. Petrusgr (talk) 20:39, 28 March 2023 (UTC)Petrusgr (talk) 21:45, 7 May 2023 (UTC)

7. I believe Groeneboom was at the editorial board of the Annals of Statistics twice, not three times. This was a mistake in the announcement of the Wald lectures. It doesn't seem very relevant either.

8. Proving consistency in the interval censoring models does not seem to be such a big deal. More important is that he proved the cube root n convergence to Chernoff"s distribution for the nonparametric MLE in the current status model and the square root n convergence and asymptotic normality of the estimate of the first moment, based on this MLE, in the same model. Both results are in the 1992 DMV seminar book with Jon Wellner. — Preceding unsigned comment added by Petrusgr (talk • contribs) 22:16, 23 May 2023 (UTC)

These seem excellent suggestions; and the facts are certainly correct. Richard Gill (talk) 05:56, 29 March 2023 (UTC)

Thank you to you and @Petrusgr for your suggestions on how to improve this article, which I am sorry I noticed only now. (You may have seen that there is a button with which you could request Wikipedia's help if there had been, or if there are at any time, statements you deemed wrong.) Some of the issues come down to me not having familiarized myself very well with Groeneboom's research. I hope that what is now in the article is acceptable also from an expert point of view. Let me offer my thoughts on your list:

0) I think the mention of the candidate degree is noteworthy and thus merits inclusion in Wikipedia; not because of it being a degree per se, but because a shift between fields as distant as psychology and mathematics, also given that Groeneboom completed his degree in the former, seems not all too common.

1) I figured (as far as I can recall after these months) it would increase the chances of getting this draft article accepted if I cross-reference to what is already there, namely the article on comparison of topologies, also in order to make the article appear less specialist.

2) Perhaps I will be able to get a hand on the Schneider reference. The problem with the other references, in my view, is that Groeneboom is an author or co-author, which would up the number of primary references – which Wikipedia appears to not encourage, even though academic work is refereed.

3)–5) similar as in 2).

6) I had noticed the other affiliations but decided to leave them out of the infobox. Perhaps they could be mentioned in the running text. They are in my view qualitatively different as they were "Visiting" Professorships.

7) Thank you for pointing out this error. I have deleted the sentence in question.

8) Thank you again. (See my remarks at the beginning.) I have deleted the bit about consistency. I think that the mention of the work in relation to the Chernoff distribution is relatively complete and thus may (if only barely) suffice to make the point you raise.--CRau080 (talk) 08:05, 13 July 2023 (UTC)

Great to see this published

You worked hard on this one @CRau080 - good to see all those references woven in. Nice piece! MatthewDalhousie (talk) 04:11, 13 July 2023 (UTC)

Thank you for your praise for this, and again for having made some edits yourself. I was far from being the best person to write this article. But that it had to be there, from my grasp of Wikipedia, is something that I was reasonably, if not fully, confident about from the outset. I am at present not sure if or when I will write more mathematician biographical articles, but these words should certainly not be taken as intending to scare off others; I certainly found the work on the draft rewarding.--CRau080 (talk) 08:12, 13 July 2023 (UTC)