mcsm (version 1.0)

jamestein: Monte Carlo plots of the risks of James-Stein estimators

Description

This is a Monte-Carlo representation of the risks of some James-Stein estimators of the mean $theta$ of a p-dimensional $N(theta,I)$ distribution, taking advantage of a variance reduction principle based on recycling random variates.

Usage

jamestein(N = 10^3, p = 5)

Arguments

N

Number of simulations

p

Dimension of the problem

Value

Returns a plot with 10 different values of the shrinkage factor $a$ between 1 and $2*(p-2)$, which is the maximal possible value for minimaxity.

Warning

Because of the multiple loops used in the code, this program takes quite a while to produce its outcome. Note that there is a James-Stein effect only when $p>2$ but that it may not be visible for a small value of N.

Details

Given that the risk is computed for all values of the mean $theta$, using a different normal sample for each value of $theta$ creates an extraneous noise that is unecessary. Using the same sample produces a smooth and well-ordered (in the shrinkage parameter $a$) set of graphs.

References

Chapter 4 of EnteR Monte Carlo Statistical Methods

Examples

jamestein(N=2*10^2)     #N is too small to show minimaxity