Kiefer Wolfowitz NPMLE for Student t location mixtures
TLmix(x, v = 300, u = 300, df = 1, hist = FALSE, weights = NULL, ...)An object of class density with components:
midpoints of evaluation on the domain of the mixing density
estimated function values at the points x of the mixing density
Log likelihood value at the proposed solution
Bayes rule estimates of location at x
Mosek exit code
Data: Sample Observations
bin boundaries defaults to equal spacing of length v
bin boundaries for histogram binning: defaults to equal spacing
Number of degrees of freedom of Student base density
If TRUE then aggregate x to histogram weights
replicate weights for x obervations, should sum to 1
optional parameters passed to KWDual to control optimization
Roger Koenker
Kiefer Wolfowitz MLE density estimation as proposed by Jiang and Zhang for a Student t compound decision problem. The histogram option is intended for large problems, say n > 1000, where reducing the sample size dimension is desirable. By default the grid for the binning is equally spaced on the interval between the 0.01 and 0.99 quantiles of the observed sample. This is intended to avoid extreme gridding for Student's with small df.
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.
Jiang, Wenhua and Cun-Hui Zhang General maximum likelihood empirical Bayes estimation of normal means Ann. Statist., 37, (2009), 1647-1684.
Koenker, R. and J. Gu, (2017) REBayes: An R Package for Empirical Bayes Mixture Methods, Journal of Statistical Software, 82, 1--26.
GLmix for Gaussian version