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, ...)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
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
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