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