Kiefer Wolfowitz NPMLE for Student t non-centrality parameter mixtures Model: \(y_{ig} = mu_{g} + e_{ig}, e_{ig} ~ N(0,sigma_{g}^{2})\) x is the vector of t statistics for all groups, which follows t dist if \(mu_g = 0\), and noncentral t dist if \(mu_g \neq 0\), with \(ncp_{g} = \mu_g / \sigma_{g}\). This leads to a mixture of t distribution with ncp as the mixing parameter. df (degree of freedom) is determined by the group size in the simplest case.
Tncpmix(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
estimated function values at the observed points of mixture 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, 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 J. Gu, (2017) REBayes: An R Package for Empirical Bayes Mixture Methods, Journal of Statistical Software, 82, 1--26.
GLmix for Gaussian version