Interior point solution of Kiefer-Wolfowitz NPMLE for mixture of binomials
Bmix(x, k, v = 300, collapse = TRUE, weights = NULL, ...)Count of "successes" for binomial observations
Number of trials for binomial observations
Grid Values for the mixing distribution defaults to equal spacing of length v on [eps, 1- eps], if v is scalar.
Collapse observations into cell counts.
replicate weights for x obervations, should sum to 1
Other arguments to be passed to KWDual to control optimization
An object of class density with components:
grid midpoints of evaluation of the mixing density
function values of the mixing density at x
estimates of the mixture density at the distinct data values
Log Likelihood value at the estimate
Bayes rule estimates of binomial probabilities for distinct data values
exit code from the optimizer
The predict method for Bmix 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).
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.
Koenker, R and I. Mizera, (2013) ``Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules,'' JASA, 109, 674--685.
Koenker, R. and J. Gu, (2017) REBayes: An R Package for Empirical Bayes Mixture Methods, Journal of Statistical Software, 82, 1--26.