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A note on Monte Carlo maximization by the density ratio model

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A note on Monte Carlo maximization by the density ratio model. / Fokianos, K.; Qin, J.
In: Journal of Statistical Theory and Practice, Vol. 2, No. 3, 2008, p. 355-367.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Fokianos, K & Qin, J 2008, 'A note on Monte Carlo maximization by the density ratio model', Journal of Statistical Theory and Practice, vol. 2, no. 3, pp. 355-367. https://doi.org/10.1080/15598608.2008.10411880

APA

Fokianos, K., & Qin, J. (2008). A note on Monte Carlo maximization by the density ratio model. Journal of Statistical Theory and Practice, 2(3), 355-367. https://doi.org/10.1080/15598608.2008.10411880

Vancouver

Fokianos K, Qin J. A note on Monte Carlo maximization by the density ratio model. Journal of Statistical Theory and Practice. 2008;2(3):355-367. doi: 10.1080/15598608.2008.10411880

Author

Fokianos, K. ; Qin, J. / A note on Monte Carlo maximization by the density ratio model. In: Journal of Statistical Theory and Practice. 2008 ; Vol. 2, No. 3. pp. 355-367.

Bibtex

@article{5b4b69bed7be4a288617cf1a5d73392f,
title = "A note on Monte Carlo maximization by the density ratio model",
abstract = "It is well known that untractable normalizing constants of probability density functions complicate the calculation of maximum likelihood estimators. Usually numerical or Monte Carlo methods are employed in order to obtain an approximation to the solution of the likelihood equations. We propose a new statistical method for carrying out the calculations regarding maximum likelihood estimation by avoiding the explicit calculation of any normalizing constant. We formulate the problem within the framework of semiparametric maximum likelihood estimation for a two samples model, where the ratio of two densities is known up to some parameters, but the form of the two densities are unknown and one of the sample sizes can be chosen arbitrarily large. The two-sample semiparametric model-which is referred as density ratio model-arises naturally in case-control studies. Statistical inference techniques are developed for this model. Comparisons between the proposed method and the conventional estimated pseudo-likelihood method are studied.",
keywords = "Biased sampling, empirical likelihood, density ratio model, likelihood ratio, normalizing constant",
author = "K. Fokianos and J. Qin",
year = "2008",
doi = "10.1080/15598608.2008.10411880",
language = "English",
volume = "2",
pages = "355--367",
journal = "Journal of Statistical Theory and Practice",
issn = "1559-8608",
publisher = "Taylor and Francis",
number = "3",

}

RIS

TY - JOUR

T1 - A note on Monte Carlo maximization by the density ratio model

AU - Fokianos, K.

AU - Qin, J.

PY - 2008

Y1 - 2008

N2 - It is well known that untractable normalizing constants of probability density functions complicate the calculation of maximum likelihood estimators. Usually numerical or Monte Carlo methods are employed in order to obtain an approximation to the solution of the likelihood equations. We propose a new statistical method for carrying out the calculations regarding maximum likelihood estimation by avoiding the explicit calculation of any normalizing constant. We formulate the problem within the framework of semiparametric maximum likelihood estimation for a two samples model, where the ratio of two densities is known up to some parameters, but the form of the two densities are unknown and one of the sample sizes can be chosen arbitrarily large. The two-sample semiparametric model-which is referred as density ratio model-arises naturally in case-control studies. Statistical inference techniques are developed for this model. Comparisons between the proposed method and the conventional estimated pseudo-likelihood method are studied.

AB - It is well known that untractable normalizing constants of probability density functions complicate the calculation of maximum likelihood estimators. Usually numerical or Monte Carlo methods are employed in order to obtain an approximation to the solution of the likelihood equations. We propose a new statistical method for carrying out the calculations regarding maximum likelihood estimation by avoiding the explicit calculation of any normalizing constant. We formulate the problem within the framework of semiparametric maximum likelihood estimation for a two samples model, where the ratio of two densities is known up to some parameters, but the form of the two densities are unknown and one of the sample sizes can be chosen arbitrarily large. The two-sample semiparametric model-which is referred as density ratio model-arises naturally in case-control studies. Statistical inference techniques are developed for this model. Comparisons between the proposed method and the conventional estimated pseudo-likelihood method are studied.

KW - Biased sampling

KW - empirical likelihood

KW - density ratio model

KW - likelihood ratio

KW - normalizing constant

U2 - 10.1080/15598608.2008.10411880

DO - 10.1080/15598608.2008.10411880

M3 - Journal article

VL - 2

SP - 355

EP - 367

JO - Journal of Statistical Theory and Practice

JF - Journal of Statistical Theory and Practice

SN - 1559-8608

IS - 3

ER -