Localpiecewise linear regression

Localpiecewise linear regression

In this paper, we propose a new nonparametric estimator called the local piecewise linear regression estimator. The proposed estimator has the advantages of the regression spline and the local linear regression estimator but overcomes the drawbacks of both. Here we study the asymptotic behavior of t...

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Veröffentlicht in:Journal of nonparametric statistics 1999-01, Vol.12 (1), p.63-75
Hauptverfasser: Zhou, Shanggang, Wolfe, Douglas A.
Format: Artikel
Sprache:eng
Schlagworte:
asymptotic bias
asymptotic variance
boundary effects
kernel estimator
Local piecewise linear regression
local polynomial regression
regression spline
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container_title Journal of nonparametric statistics
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creator Zhou, Shanggang
Wolfe, Douglas A.
description In this paper, we propose a new nonparametric estimator called the local piecewise linear regression estimator. The proposed estimator has the advantages of the regression spline and the local linear regression estimator but overcomes the drawbacks of both. Here we study the asymptotic behavior of the proposed estimator. Under suitable conditions, we derive the leading bias and variance terms of the local piecewise linear regression estimator at the interior and boundary points for both the fixed design and the random design. As a result, we are able to see clearly many optimal properties of the local piecewise linear regression estimator. For example, the proposed estimator is efficient, designadaptive and computationally inexpensive, and it suffers no boundary effects.
doi_str_mv 10.1080/10485259908832800
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subjects asymptotic bias
asymptotic variance
boundary effects
kernel estimator
Local piecewise linear regression
local polynomial regression
regression spline
title Localpiecewise linear regression
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