Multivariate plug-in bandwidth for local linear regression

Arbeitspapier

Optimal bandwidths for local polynomial regression usually involve functionals of the derivatives of the unknown regression function. In the multivariate case, estimates of these functionals are not readily available, primarily because estimating multivariate derivatives is complicated. In this paper, an estimator of multivariate second derivative is obtained via local quadratic regression with cross terms left out. This estimator has the optimal rate of convergence but is simpler and uses a lot less computing time than the full local quadratic estimator. Using this as a pilot estimator, an estimator of the integrated squared Laplacian of a multivariate regression function is obtained which leads to a plug-in formula of the optimal bandwidth for multivariate local linear regression. This bandwidth has good theoretical properties as well as satisfactory performance in our simulation study. It is also recommended for variable selection methods.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: SFB 373 Discussion Paper ; No. 1997,99

Klassifikation und Themen

• Klassifikation: Wirtschaft
• Thema: Bandwidth selection ; Asymptotic optimality ; Functional estimation ; Laplacian ; Local quadratic regression ; Second derivatives ; Within bias trade off

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Yang, Lijian ; Tschernig, Rolf
• Ereignis: Veröffentlichung
• (wer): Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes
• (wo): Berlin
• (wann): 1997

Weitere Informationen

• Handle: http://hdl.handle.net/10419/66265
• URN: urn:nbn:de:kobv:11-10064769
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ