Poisson mixture estimation via Kiefer Wolfowitz MLE
Pmix(x, v = 300, support = NULL, exposure = NULL, ...)An object of class density with components:
points of evaluation of the mixing density
function values of the mixing density at x
function values of the mixture density on \(0, 1, ... max(x)+1\)
Log Likelihood value at the estimate
Bayes rule estimate of Poisson rate parameter at each x
exit code from the optimizer
Data: Sample observations (integer valued)
Grid Values for the mixing distribution defaults to equal spacing of length v when v is specified as a scalar
a 2-vector containing the lower and upper support points of sample observations to account for possible truncation.
observation specific exposures to risk see details
other parameters passed to KWDual to control optimization
Roger Koenker and Jiaying Gu
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).
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.