NPmix {REBayes}

Normal mixture with Poisson sample size via Kiefer Wolfowitz NPMLE

Description

Interior point solution of Kiefer-Wolfowitz NPMLE for mixture of Normal/Poissons

Usage

NPmix(x, m, v = 50, u = 50, weights = NULL, ...)

Arguments

x

observed response for Gaussian observations

m

Number of trials for Poisson observations

v

Grid Values for the Gaussian means mixing distribution defaults to equal spacing of length v on [min(x) + eps, max(x) - eps], if v is scalar.

u

Grid Values for the Poisson rate mixing distribution defaults to equal spacing of length u on [min(m) + eps, max(m) - eps], if u is scalar.

weights

replicate weights for x obervations, should sum to 1

...

Other arguments to be passed to KWDual to control optimization

Details

The joint distribution of the means and the number of trials determining sample standard deviations is estimated. The grid specification for means is as for GLmix whereas the grid for the Poisson rate parameters by default depends on the support of the observed trials. There is no predict method as yet. See demo(NPmix1).

Value

An object of class density with components:

v

grid points of evaluation of the success probabilities

u

grid points of evaluation of the Poisson rate for number of trials

y

function values of the mixing density at (v,u)

g

estimates of the mixture density at the distinct data values

logLik

Log Likelihood value at the estimate

status

exit code from the optimizer

Author(s)

R. Koenker and J. Gu

References

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