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

Chen, Hung

Ann. Stat. 23, No. 4, 1102-1129 (1995).

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

Keywords:

partial spline model; maximum likelihood estimator; consistency; regression splines; semiparametric generalized linear models