[YPNG] YPNG Friday 9 Nov 2018, from 11:00--1:00

[David Pollard]

Folks,

Once again I will fill in, just to avoid a YPNG vacuum.

I'll talk about an interesting minimax result of Tony Cai and Mark Low from 2011
( https://projecteuclid.org/euclid.aos/1302268085 <https://projecteuclid.org/euclid.aos/1302268085> ). You will learn about the 
best polynomial approximation p_n to the function f(x)=|x| for -1 \le  x \le 1. 
There are some cunning probability distributions living on the set of points where
|f(x)-p_n(x)| is maximized. These nasty guys can be used to construct two prior distributions
for the vector of means in the N(\theta,I_n) distribution,  priors that cause trouble for
estimation of the L1 norm of \theta under squared error loss.

David

ps. Nice facts about Chebyshev and Hermite will be explained.
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