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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Format: | Article |
Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2004-11-01
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Series: | Revstat Statistical Journal |
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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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first_indexed | 2024-04-13T03:10:28Z |
format | Article |
id | doaj.art-0558f174c7204293891bd22708acf242 |
institution | Directory Open Access Journal |
issn | 1645-6726 2183-0371 |
language | English |
last_indexed | 2024-04-13T03:10:28Z |
publishDate | 2004-11-01 |
publisher | Instituto Nacional de Estatística | Statistics Portugal |
record_format | Article |
series | Revstat Statistical Journal |
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 |