Optimal smoothing in semiparametric index approximation of regression functions

Arbeitspapier

The problem of approximating a general regression function m(x) = E (Y IX = x) is addressed. As in the case of the c1assical L2-type projection pursuit regression considered by Hall (1989), we propose to approximate m(x) through a regression of Y given an index, that is a unidimensional projection of X. The orientation vector defining the projection of X is taken to be the optimum of a Kullback-Leibler type criterion. The first step of the c1assical projection pursuit regression and the single-index models (SIM) are obtained as particular cases. We define a kernel-based estimator of the 'optimal' orientation vector and we suggest a simple empirical bandwidth selection rule. Finally, the true regression function m(•) is approximated through a kernel regression of Y given the estimated index. Our procedure extends the idea of Härdle, Hall and Ichimura (1993) which propose, in the case of SIM, to minimize an empirical L2-type criterion simultaneously with respect to the orientation vector and the bandwidth. We show that a same bandwidth of order n - 1/5 can be used for the root-n estimation of the orientation and for the kernel approximation of the true regression function. Our methodology could be extended to more accurate multi-index approximations.

Objekt anzeigen

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: SFB 373 Discussion Paper ; No. 2000,4

Klassifikation und Themen

• Klassifikation: Wirtschaft

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Delecroix, Michel ; Hristache, Marian ; Patilea, Valentin
• Ereignis: Veröffentlichung
• (wer): Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes
• (wo): Berlin
• (wann): 2000

Weitere Informationen

• Handle: http://hdl.handle.net/10419/62179
• URN: urn:nbn:de:kobv:11-10047078