Based on a (basic) question on X validated, I re-read Halmos‘ (1946) famous paper on the non-existence of centred moments of order larger than the sample size. While the exposition may sound a wee bit daunting, the reasoning is essentially based on a recursion and the binomial theorem, since expanding the kth power leads to lesser moments, all of which can be estimated from a subsample.
Archive for Paul Halmos
re-reading Halmos (1946)
Posted in Books, Kids, Statistics, University life with tags central moments, cross validated, Paul Halmos, unbiasedness on May 16, 2020 by xi'anMy black notepad
Posted in Books, University life with tags notepad, Paul Halmos on March 22, 2010 by xi'an
“I write notes to myself, explicit ones, with sentences, not just “try power series expansion” or “see Dunford-Schwartz for
.” I think by writing… When I started to prove theorems (the acceptably low-key phrase for the more stuffy-sounding “doing research”), I would keep writing, as if I was conducting a conversation between me and myself.” Paul R. Halmos, I Want to Be a Mathematician: An Automathography, 1985.
