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Maximum likelihood estimation for semiparametric density ratio model.
Int J Biostat 2012; 8(1)IJ

Abstract

In the statistical literature, the conditional density model specification is commonly used to study regression effects. One attractive model is the semiparametric density ratio model, under which the conditional density function is the product of an unknown baseline density function and a known parametric function containing the covariate information. This model has a natural connection with generalized linear models and is closely related to biased sampling problems. Despite the attractive features and importance of this model, most existing methods are too restrictive since they are based on multi-sample data or conditional likelihood functions. The conditional likelihood approach can eliminate the unknown baseline density but cannot estimate it. We propose efficient estimation procedures based on the nonparametric likelihood. The nonparametric likelihood approach allows for general forms of covariates and estimates the regression parameters and the baseline density simultaneously. Therefore, the nonparametric likelihood approach is more versatile than the conditional likelihood approach especially when estimation of the conditional mean or other quantities of the outcome is of interest. We show that the nonparametric maximum likelihood estimators are consistent, asymptotically normal, and asymptotically efficient. Simulation studies demonstrate that the proposed methods perform well in practical settings. A real example is used for illustration.

Authors+Show Affiliations

George Mason University, USA.No affiliation info availableNo affiliation info available

Pub Type(s)

Journal Article
Research Support, N.I.H., Extramural

Language

eng

PubMed ID

22745024

Citation

Diao, Guoqing, et al. "Maximum Likelihood Estimation for Semiparametric Density Ratio Model." The International Journal of Biostatistics, vol. 8, no. 1, 2012.
Diao G, Ning J, Qin J. Maximum likelihood estimation for semiparametric density ratio model. Int J Biostat. 2012;8(1).
Diao, G., Ning, J., & Qin, J. (2012). Maximum likelihood estimation for semiparametric density ratio model. The International Journal of Biostatistics, 8(1), doi:10.1515/1557-4679.1372.
Diao G, Ning J, Qin J. Maximum Likelihood Estimation for Semiparametric Density Ratio Model. Int J Biostat. 2012 Jun 27;8(1) PubMed PMID: 22745024.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Maximum likelihood estimation for semiparametric density ratio model. AU - Diao,Guoqing, AU - Ning,Jing, AU - Qin,Jing, Y1 - 2012/06/27/ PY - 2012/6/30/entrez PY - 2012/6/30/pubmed PY - 2012/12/10/medline JF - The international journal of biostatistics JO - Int J Biostat VL - 8 IS - 1 N2 - In the statistical literature, the conditional density model specification is commonly used to study regression effects. One attractive model is the semiparametric density ratio model, under which the conditional density function is the product of an unknown baseline density function and a known parametric function containing the covariate information. This model has a natural connection with generalized linear models and is closely related to biased sampling problems. Despite the attractive features and importance of this model, most existing methods are too restrictive since they are based on multi-sample data or conditional likelihood functions. The conditional likelihood approach can eliminate the unknown baseline density but cannot estimate it. We propose efficient estimation procedures based on the nonparametric likelihood. The nonparametric likelihood approach allows for general forms of covariates and estimates the regression parameters and the baseline density simultaneously. Therefore, the nonparametric likelihood approach is more versatile than the conditional likelihood approach especially when estimation of the conditional mean or other quantities of the outcome is of interest. We show that the nonparametric maximum likelihood estimators are consistent, asymptotically normal, and asymptotically efficient. Simulation studies demonstrate that the proposed methods perform well in practical settings. A real example is used for illustration. SN - 1557-4679 UR - https://www.unboundmedicine.com/medline/citation/22745024/Maximum_likelihood_estimation_for_semiparametric_density_ratio_model_ L2 - https://www.degruyter.com/doi/10.1515/1557-4679.1372 DB - PRIME DP - Unbound Medicine ER -