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August 1997 On automatic boundary corrections
Ming-Yen Cheng, Jianqing Fan, J. S. Marron
Ann. Statist. 25(4): 1691-1708 (August 1997). DOI: 10.1214/aos/1031594737


Many popular curve estimators based on smoothing have difficulties caused by boundary effects. These effects are visually disturbing in practice and can play a dominant role in theoretical analysis. Local polynomial regression smoothers are known to correct boundary effects automatically. Some analogs are implemented for density estimation and the resulting estimators also achieve automatic boundary corrections. In both settings of density and regression estimation, we investigate best weight functions for local polynomial fitting at the endpoints and find a simple solution. The solution is universal for general degree of local polynomial fitting and general order of estimated derivative. Furthermore, such local polynomial estimators are best among all linear estimators in a weak minimax sense, and they are highly efficient even in the usual linear minimax sense.


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Ming-Yen Cheng. Jianqing Fan. J. S. Marron. "On automatic boundary corrections." Ann. Statist. 25 (4) 1691 - 1708, August 1997.


Published: August 1997
First available in Project Euclid: 9 September 2002

zbMATH: 0890.62026
MathSciNet: MR1463570
Digital Object Identifier: 10.1214/aos/1031594737

Primary: 62G07
Secondary: 62C20

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 4 • August 1997
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