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On the shrinkage of local linear curve estimators

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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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Authors and Affiliations

  1. Centre for Mathematics and its Applications, Australian National University, Canberra, ACT, 0200, Australia

    Peter Hall

  2. Institute of Mathematical Statistics, National Chung Cheng University, Minghsiung, Chiayi, Taiwan, Republic of China

    Ming-Yen Cheng

  3. Department of Statistics, University of Glasgow, Glasgow, G12 8QW, UK

    D. M. Titterington

Authors
  1. Ming-Yen Cheng
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  2. Peter Hall
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  3. D. M. Titterington
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Cheng, MY., Hall, P. & Titterington, D.M. On the shrinkage of local linear curve estimators. Statistics and Computing 7, 11–17 (1997). https://doi.org/10.1023/A:1018549127542

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