ArticleOriginal scientific text
Title
An approximate necessary condition for the optimal bandwidth selector in kernel density estimation
Authors 1, 2
Affiliations
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
- Institute of Mathematics, technical University of Łódź, Al. Politechniki 11, 90-924 Łódź, Poland
Abstract
An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.
Keywords
bandwidth selection, kernel density estimation, resampling
Bibliography
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- W. Härdle, P. Hall and J. S. Marron (1988), How far are automatically chosen regression smoothing parameters from their optimum? (with comments), ibid. 74, 105-131
- C. Léger, D. N. Politis and J. P. Romano (1992), Bootstrap technology and applications, Technometrics 43, 378-398
- E. Parzen (1962), On estimation of a probability density function and mode, Ann. Math. Statist. 33, 1065-1076
- M. Rosenblatt (1956), Remarks on some nonparametric estimates of a density function, ibid. 27, 832-837
- B. W. Silverman (1986), Density Estimation for Statistics and Data Analysis, Chapman and Hall, London
- C. C. Taylor (1989), Bootstrap choice of the smoothing parameter in kernel density estimation, Biometrika 76, 705-712.
Pages:
123-138
Main language of publication
English
Received
1993-06-24
Accepted
1993-09-10
Published
1993
Exact and natural sciences