Local fitting with a power basis

Local polynomial modelling can be seen as a local fit of the data against a polynomial basis. In this paper we extend this method to the power basis, i.e. a basis which consists of the powers of an arbitrary function. Using an extended Taylor theorem, we derive asymptotic expressions for bias and v...

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Main Author: Jochen Einbeck
Format: Article
Language:English
Published: Instituto Nacional de Estatística | Statistics Portugal 2004-11-01
Series:Revstat Statistical Journal
Subjects:
Online Access:https://revstat.ine.pt/index.php/REVSTAT/article/view/10
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author Jochen Einbeck
author_facet Jochen Einbeck
author_sort Jochen Einbeck
collection DOAJ
description Local polynomial modelling can be seen as a local fit of the data against a polynomial basis. In this paper we extend this method to the power basis, i.e. a basis which consists of the powers of an arbitrary function. Using an extended Taylor theorem, we derive asymptotic expressions for bias and variance of this estimator. We apply this method to a simulated data set for various basis functions and discuss situations where the fit can be improved by using a suitable basis. Finally, some remarks about bandwidth selection are given and the method is applied to real data.
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spelling doaj.art-0558f174c7204293891bd22708acf2422022-12-22T03:05:05ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712004-11-012210.57805/revstat.v2i2.10Local fitting with a power basis Jochen Einbeck 0Ludwig Maximilians University Munich Local polynomial modelling can be seen as a local fit of the data against a polynomial basis. In this paper we extend this method to the power basis, i.e. a basis which consists of the powers of an arbitrary function. Using an extended Taylor theorem, we derive asymptotic expressions for bias and variance of this estimator. We apply this method to a simulated data set for various basis functions and discuss situations where the fit can be improved by using a suitable basis. Finally, some remarks about bandwidth selection are given and the method is applied to real data. https://revstat.ine.pt/index.php/REVSTAT/article/view/10local polynomial fittingTaylor expansionpower basisbias reduction
spellingShingle Jochen Einbeck
Local fitting with a power basis
Revstat Statistical Journal
local polynomial fitting
Taylor expansion
power basis
bias reduction
title Local fitting with a power basis
title_full Local fitting with a power basis
title_fullStr Local fitting with a power basis
title_full_unstemmed Local fitting with a power basis
title_short Local fitting with a power basis
title_sort local fitting with a power basis
topic local polynomial fitting
Taylor expansion
power basis
bias reduction
url https://revstat.ine.pt/index.php/REVSTAT/article/view/10
work_keys_str_mv AT jocheneinbeck localfittingwithapowerbasis