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Feb 2000 Skewing methods for two-parameter locally parametric density estimation
Ming-Yen Cheng, Edwin Choi, Jianqing Fan, Peter Hall
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Bernoulli 6(1): 169-182 (Feb 2000).


A `skewing' method is shown to effectively reduce the order of bias of locally parametric estimators, and at the same time retain positivity properties. The technique involves first calculating the usual locally parametric approximation in the neighbourhood of a point x' that is a short distance from the place x where the we wish to estimate the density, and then evaluating this approximation at x. By way of comparison, the usual locally parametric approach takes x'=x. In our construction, x'-x depends in a very simple way on the bandwidth and the kernel, and not at all on the unknown density. Using skewing in this simple form reduces the order of bias from the square to the cube of bandwidth; and taking the average of two estimators computed in this way further reduces bias, to the fourth power of bandwidth. On the other hand, variance increases only by at most a moderate constant factor.


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Ming-Yen Cheng. Edwin Choi. Jianqing Fan. Peter Hall. "Skewing methods for two-parameter locally parametric density estimation." Bernoulli 6 (1) 169 - 182, Feb 2000.


Published: Feb 2000
First available in Project Euclid: 22 April 2004

zbMATH: 0944.62035
MathSciNet: MR2001H:62062

Keywords: bias reduction , kernel methods , Local least squares , local likelihood , local linear methods , score function , weighted least squares

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability

Vol.6 • No. 1 • Feb 2000
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