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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.

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