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Profile likelihood and conditionally parametric models. (English) Zbl 0768.62015
The authors 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 C. Stein [Proc. Third Berkeley Sympos. Math. Statist. Probability 1, 187-195 (1956; Zbl 0074.34801)]. The likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for that parameter. 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.

62F10 Point estimation
62F35 Robustness and adaptive procedures (parametric inference)
62G07 Density estimation
62F12 Asymptotic properties of parametric estimators
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