TLmix {REBayes}

NPMLE for Student t location mixtures

Description

Kiefer Wolfowitz NPMLE for Student t location mixtures

Usage

TLmix(x, v = 300, u = 300, df = 1, hist = FALSE, weights = NULL, ...)

Arguments

x

Data: Sample Observations

v

bin boundaries defaults to equal spacing of length v

u

bin boundaries for histogram binning: defaults to equal spacing

df

Number of degrees of freedom of Student base density

hist

If TRUE then aggregate x to histogram weights

weights

replicate weights for x obervations, should sum to 1

...

optional parameters passed to KWDual to control optimization

Details

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.

Value

An object of class density with components:

x

midpoints of evaluation on the domain of the mixing density

y

estimated function values at the points x of the mixing density

logLik

Log likelihood value at the proposed solution

dy

Bayes rule estimates of location at x

status

Mosek exit code

Author(s)

Roger Koenker

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.

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.

See Also

GLmix for Gaussian version