Pmix: Poisson mixture estimation via Kiefer Wolfowitz MLE

In REBayes: Empirical Bayes Estimation and Inference

Poisson mixture estimation via Kiefer Wolfowitz MLE

Description

Poisson mixture estimation via Kiefer Wolfowitz MLE

Usage

Pmix(x, v = 300, support = NULL, exposure = NULL, ...)

Arguments

x	Data: Sample observations (integer valued)
v	Grid Values for the mixing distribution defaults to equal spacing of length v when v is specified as a scalar
support	a 2-vector containing the lower and upper support points of sample observations to account for possible truncation.
exposure	observation specific exposures to risk see details
...	other parameters passed to KWDual to control optimization

Details

The predict method for Pmix objects will compute means, medians or modes of the posterior according to whether the Loss argument is 2, 1 or 0, or posterior quantiles if Loss is in (0,1).

In the default case exposure = 1 it is assumed that x contains individual observations that are aggregated into count bins via table. When exposure has the same length as x then it is presumed to be individual specific risk exposure and the Poisson mixture is taken to be x | v ~ Poi(v * exposure) and the is not aggregated. See for example the analysis of the Norberg data in Koenker and Gu (2016).

Value

An object of class density with components:

x	points of evaluation of the mixing density
y	function values of the mixing density at x
g	function values of the mixture density on 0, 1, ... max(x)+1
logLik	Log Likelihood value at the estimate
dy	Bayes rule estimate of Poisson rate parameter at each x
status	exit code from the optimizer

Author(s)

Roger Koenker and Jiaying Gu

References

Kiefer, J. and J. Wolfowitz Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters Ann. Math. Statist. Volume 27, Number 4 (1956), 887-906.

Koenker, R. and J. Gu, (2017) REBayes: An R Package for Empirical Bayes Mixture Methods, Journal of Statistical Software, 82, 1–26.

REBayes documentation built on Aug. 19, 2023, 5:10 p.m.