User talk:Petrusgr

Welcome!

Hello, Petrusgr, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

The five pillars of Wikipedia
Tutorial
How to edit a page and How to develop articles
How to create your first article (using the Article Wizard if you wish)
Simplified Manual of Style

I hope you enjoy editing here and being a Wikipedian! Please sign your messages on talk pages using four tildes (~~~~); this will automatically insert your username and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question on this page and then place {{help me}} before the question. Again, welcome!

Greetings

Hi Petrus Gr!

That was an excellent start you made to the talk page of the draft article on Piet Groeneboom. Richard Gill (talk) 05:54, 29 March 2023 (UTC)[reply]

Thanks Richard Gill! I still want to add to point 2 of the account that in the 1988 paper in PTRF on convex hulls of samples in the plane by Piet Groeneboom also central limit theorems for the vertices of convex hulls of uniform samples in the interior of convex sets with smooth boundaries (circles, ellipses) were proved. The rate changes from sqrt(log n) to n^{1/3} in that case. This is also mentioned in Chapter 12 of the Handbook of Discrete and Computational Geometry (2017), written by Rolf Schneider.

Concerning point 3: the property one needs in proving the conjecture of Perlman and Olkin ("power of the test is monotone in the eigenvalues of the non-centrality matrix"), following their approach is called "pairwise TP_2". One needs this if one wants to apply the FKG inequality. But unfortunately, the "pairwise TP_2" property does not hold, as shown in the Indagationes (2000) paper (an unchanged version of the 1983 MSRI report), so bad luck for the persons who tried it that way. Michael Perlman had a stack of these MSRI reports in his drawer, to send to people who sent him false proofs of this type. Petrusgr (talk) 07:47, 29 March 2023 (UTC)[reply]