Semi-parametric estimation of generalized partially linear single-index models - Yingcun Xia; Wolfgang Härdle (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2002)
One of the most difficult problems in applications of semiparametric generalized partially linear single-index model (GPLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root-n consistent, although they are not given in a constructible way. Complexity parameters, such as a smoothing bandwidth are constrained to a certain speed, which is rarely determinable in practical situations. In this paper, efficient, constructible and practicable estimators of GPLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. (1997): no root-n pilot estimator for the single index part of the model is needed and complexity parameters can be selected at the optimal smoothing rate. The asymptotic distribution is derived and the corresponding algorithm is easily implemented. Examples from real data sets (credit-scoring and environmental statistics) illustrate the technique and the proposed methodology of minimum average variance estimation (MAVE).
urn:nbn:de:kobv:11-10049145
Keywords: 330; Asymptotic distribution; Generalized partially linear model; Local linear smoother; Optimal consistency rate; Single-index model