The Amount of Noise Inherent in Bandwidth Selection for a Kernel Density Estimator.
Technical rept. Sep 84-Aug 85,
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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Any practical method of constructing a bandwidth must depend only on a statistical sample, and should produce some sort of estimate of this bandwidth. The purpose of this paper is to show that there a well-defined limits to the accuracy of all data-driven bandwidth estimates. Put another way, there is an unbridgeable gap between the minimum integrated square error attained using a optimal bandwidth and the minimum achievable integrated square error using a data-driven bandwidth estimate. Additional keywords stochastic processes cross validation and random variables.
- Statistics and Probability