GaussianNPML: Nonparametric Maximum Likelihood estimation, Gaussian

In gregridgeway/hhsim: Hierarchical model simulation functions

Description

Implements the nonparametric maximum likelihood estimation (NPML) estimate of g(theta).

Usage

GaussianNPML(Y,
             sigma2=rep(1,length(Y)),
             mu=Y,
             alpha=rep(1/length(Y),length(Y)),
             tolerance=0.0001,
             verbose=FALSE)

Arguments

Y	vector of data points
sigma2	vector of known variances
mu	vector of initial mass points for the NPML
alpha	vector of initial weights on each mass point, mu
tolerance	absolute change in thetas before considered converged
verbose	indicator of whether to print progress information

Details

Assumes a model of the form Y[k]~N(theta[k],sigma[k]) where theta[k]~g(theta). This function gets posterior means for theta using the NPML estimate for g. It uses the EM algorithm to solve for g. No attempt is made to merge very close mass points since our main interest is in estimates of theta[k].

Value

theta	empirical Bayes posterior mean estimates of theta
sigma2	estimates of sigma2 (currently not estimated, assumed known)
mu	mass points from the NPML
alpha	probability mass for each mu

Author(s)

Greg Ridgeway [e-mail]

References

Laird N.M. (1982). Empirical Bayes estimate using the non-parametric maximum likelihood estimate of the prior. Journal of Statistical Computation and Simulation, 15:211-220.

See Also

GaussianSBR

Examples

k <- 100
theta <- rnorm(k,0,1)
sigma <- rep(1,k)
Y <- rnorm(k,theta,sigma)

out.npml  <- GaussianNPML(Y,sigma^2)
x <- with(out.npml, sample(mu,size=100000,replace=TRUE,prob=alpha))
hist(x,main="NPML",prob=TRUE,xlab="theta",ylab="g(theta)")

plot(out.npml$theta,theta)

gregridgeway/hhsim documentation built on May 17, 2019, 8:36 a.m.