Multivariate Local Fitting with General Basis Functions

Jochen Einbeck
Additional contact information
Jochen Einbeck: Ludwig Maximilians Universität

Computational Statistics, 2003, vol. 18, issue 2, No 2, 185-203

Abstract: Summary In this paper we combine the concepts of local smoothing and fitting with basis functions for multivariate predictor variables. We start with arbitrary basis functions and show that the asymptotic variance at interior points is independent of the choice of the basis. Moreover we calculate the asymptotic variance at boundary points. We are not able to compute the asymptotic bias since a Taylor theorem for arbitrary basis functions does not exist. For this reason we focus on basis functions without interactions and derive a Taylor theorem which covers this case. This theorem enables us to calculate the asymptotic bias for interior as well as for boundary points. We demonstrate how advantage can be taken of the idea of local fitting with general basis functions by means of a simulated data set, and also provide a data-driven tool to optimize the basis.

Keywords: Bias reduction; local polynomial fitting; multivariate kernel smoothing; Taylor expansion (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s001800300140 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:18:y:2003:i:2:d:10.1007_s001800300140

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s001800300140

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().