Bias Reduction in Kernel Density Estimation via Data Sharpening
Michael C. Minnotte
Department of Statistics
Utah State University
 
Monday, October 10, 2005
4:10 p.m.
E203 Engineering Building

ABSTRACT

Kernel density estimation is an effective method for nonparametric estimation of unknown probability density functions. Unfortunately, the estimates can be strongly biased in places, especially for moderate sample sizes, which can limit their utility for some purposes. A number of approaches have been proposed to reduce the bias from the order of the smoothing parameter (h) squared, to the fourth power or higher, most commonly through the use of specially-designed higher-order kernels.

We show that data sharpening (also called variable location estimation), in which the placement of standard second-order kernels is carefully adjusted by means of a pilot estimate, provides an estimation method which is both computationally straightforward and effective by a number of measures. Theoretical and numerical results show that our method can provide appreciable improvements over higher-order kernel estimation, in terms of reduced mean squared error, reduced "wiggliness", and guaranteed positivity. (This work was joint with Peter Hall.)

[Refreshments will be served in Room 008 Statistics at 3:45 p.m.]



 

 


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