Interior point solution of Kiefer-Wolfowitz NPMLE for mixture of bivariate binomials
B2mix(x, k, u = 40, v = 40, weights = NULL, ...)An object of class density with components:
grid of evaluation points of the mixing density
grid of evaluation points 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
n by 2 matrix of counts of "successes" for binomial observations
n by 2 matrix of Number of trials for binomial observations
Grid Values for the mixing distribution defaults to equal spacing of length u on [eps, 1- eps], if u is scalar.
Grid Values for the mixing distribution defaults to equal spacing of length v on [eps, 1- eps], if v is scalar.
replicate weights for x obervations, should sum to 1
Other arguments to be passed to KWDual to control optimization
R. Koenker
This function was inspired by a paper by Kline and Walters (2019) on evaluation of audit experiments for employment discrimination. An example of its usage is available with `demo(B2mix1)`. There can be identification issues particularly when the numbers of trials are modest as described in Koenker and Gu (2024). Caveat emptor! The predict method for B2mix objects will compute posterior means,
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.
Kline, P. and C. Walters, (2019) Audits as Evidence: Experiments, Ensembles and Enforcement, preprint.
Koenker, R. and Gu, J. (2024) Empirical Bayes: Some Tools, Rules and Duals, Cambridge University Press.
`Bmix` for univariate binomial mixtures.