Linear minimax efficiency of local polynomial regression smoothers

Kani Chen

doi:10.1080/1048525031000120233

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Linear minimax efficiency of local polynomial regression smoothers

Kani Chen

Year: 2003 Journal: Journal of nonparametric statistics Vol: 15 (3)Pages: 343-353 Publisher: Taylor & Francis

DOI: 10.1080/1048525031000120233

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Abstract

This paper proves that local polynomial regression smoothers achieve linear minimax efficiency over a class of functions, generalizing a result of Fan (1993) for local linear smoothers and proving that a conjecture of Fan and Gijbels (1996) is true. Consequences are also illustrated.

Keywords:

Minimax Mathematics Polynomial regression Polynomial Class (philosophy) Applied mathematics Linear regression Conjecture Mathematical optimization Regression Local regression Statistics Combinatorics Mathematical analysis Computer science Artificial intelligence

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Advanced Optimization Algorithms Research

Physical Sciences → Mathematics → Numerical Analysis

Advanced Statistical Methods and Models

Physical Sciences → Mathematics → Statistics and Probability

Control Systems and Identification

Physical Sciences → Engineering → Control and Systems Engineering

Linear minimax efficiency of local polynomial regression smoothers

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