On the shrinkage of local linear curve estimators |
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Authors: | Cheng Ming-Yen Hall Peter Titterington D. M. |
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Affiliation: | (1) Centre for Mathematics and its Applications, Australian National University, Canberra, ACT, 0200, Australia;(2) Institute of Mathematical Statistics, National Chung Cheng University, Minghsiung, Chiayi, Taiwan, Republic of China;(3) Department of Statistics, University of Glasgow, Glasgow, G12 8QW, UK |
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Abstract: | Local linear curve estimators are typically constructed using a compactly supported kernel, which minimizes edge effects and (in the case of the Epanechnikov kernel) optimizes asymptotic performance in a mean square sense. The use of compactly supported kernels can produce numerical problems, however. A common remedy is ridging, which may be viewed as shrinkage of the local linear estimator towards the origin. In this paper we propose a general form of shrinkage, and suggest that, in practice, shrinkage be towards a proper curve estimator. For the latter we propose a local linear estimator based on an infinitely supported kernel. This approach is resistant against selection of too large a shrinkage parameter, which can impair performance when shrinkage is towards the origin. It also removes problems of numerical instability resulting from using a compactly supported kernel, and enjoys very good mean squared error properties. |
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Keywords: | Bandwidth bias compactly supported kernel kernel estimator mean squared error ridge parameter smoothing variance |
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