Cosslett: Kiefer-Wolfowitz estimator for Cosslett (1983) estimator

In REBayes: Empirical Bayes Estimation and Inference

Kiefer-Wolfowitz estimator for Cosslett (1983) estimator

Description

Kiefer-Wolfowitz-Cosslett estimator for binary response model.

Usage

Cosslett(x, y, v = 300, weights = NULL, ...)

Arguments

x	is the observed utility difference between two choices, it would be possible to extend this to make x a linear (index) function of some parameters
y	is the binary outcome
v	the unobserved utility difference taking values on a grid, by default this grid is equally spaced with 300 distinct points, however it is known that the mass points for the problem are located at the data points, x, so users may wish to set v = sort(x) although if the sample size is large this can be slow.
weights	replicate weights for x observations, should sum to 1
...	optional parameters to be passed to KWDual to control optimization

Details

In the primal form of the problem the pseudo log likelihood is:

l(f|y) = sum_i [ y_i \log \sum_j (I(v_j <= x_i) * f_j) + (1 - y_i) \log \sum_j (I(v_j > x_i) * f_j) ]

as usual the implementation used here solves the corresponding dual problem. Cumsum of the output y gives the CDF of the unobserved utility difference. See the demo(Cosslett1)and demo(Cosslett2) for illustrations without any covariate, and demo(Cosslett3) for an illustration with a covariate using profile likelihood. This model is also known as current status linear regression in the biostatistics literature, see e.g. Groeneboom and Hendrickx (2016) for recent results and references.

Value

an object of class density with the components:

x	points of evaluation of the mixing density
y	function values of the mixing density at x
logL	log likelihood of estimated model
status	exit code from the optimizer

Author(s)

Jiaying Gu and Roger Koenker

References

Kiefer, J. and J. Wolfowitz (1956) Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters, Ann. Math. Statist, 27, 887-906.

Cosslett, S. (1983) Distribution Free Maximum Likelihood Estimator of the Binary Choice Model, Econometrica, 51, 765-782.

Groeneboom, P. and K. Hendrickx (2016) Current Status Linear Regression, preprint available from https://arxiv.org/abs/1601.00202.

REBayes documentation built on Aug. 19, 2023, 5:10 p.m.