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Asymptotically efficient estimation in semiparametric generalized linear models. (English) Zbl 0838.62024

Summary: We use the method of maximum likelihood and regression splines to derive estimates of the parametric and nonparametric components of semiparametric generalized linear models. The resulting estimators of both components are shown to be consistent. Also, the asymptotic theory for the estimator of the parametric component is derived, indicating that the parametric component can be estimated efficiently without undersmoothing the nonparametric component.

MSC:

62G07 Density estimation
62J12 Generalized linear models (logistic models)
62F12 Asymptotic properties of parametric estimators
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