On the shrinkage of local linear curve estimators

  • Authors:

  • Ming-Yen Cheng;Peter Hall;D. M. Titterington

  • Affiliations:

  • Institute of Mathematical Statistics, National Chung Cheng University, Minghsiung, Chiayi, Taiwan, Republic of China;Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia;Department of Statistics, University of Glasgow, Glasgow G12 8QW, UK

  • Venue:
  • Statistics and Computing
  • Year:
  • 1997

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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.