Profile Likelihood and Conditionally Parametric Models

• Published in: The Annals of statistics Vol. 20; no. 4; pp. 1768 - 1802
• Main Authors: Severini, Thomas A., Wong, Wing Hung
• Format: Journal Article
• Language: English
• Published: Hayward, CA Institute of Mathematical Statistics 01-12-1992; The Institute of Mathematical Statistics
• Subjects: 62F10; 62F35; 62G07; Efficiency; estimation; Estimation methods; Estimators; Exact sciences and technology; Fisher information; Mathematical independent variables; Mathematics; Maximum likelihood estimation; Maximum likelihood estimators; nonparametric; Parametric inference; Parametric models; Probability and statistics; Random variables; Scalars; Sciences and techniques of general use; semiparametric; Semiparametric modeling; Statistics; Exponential family; Maximum likelihood; Asymptotic efficiency; Semiparametric model; Fisher information
• ISSN: 0090-5364; 2168-8966
• DOI: 10.1214/aos/1176348889

In this paper, we outline a general approach to estimating the parametric component of a semiparametric model. For the case of a scalar parametric component, the method is based on the idea of first estimating a one-dimensional subproblem of the original problem that is least favorable in the sense of Stein. The likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for the problem. The scalar parameter is then estimated by maximizing this "generalized profile likelihood." This method of estimation is applied to a particular class of semiparametric models, where it is shown that the resulting estimator is asymptotically efficient.