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

In mcsm: Functions for Monte Carlo Methods with R

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

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.

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.

Author(s)

Christian P. Robert and George Casella

References

Chapter 4 of EnteR Monte Carlo Statistical Methods

Examples

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

Example output

Loading required package: MASS
Loading required package: coda

mcsm documentation built on May 2, 2019, 10:16 a.m.