Inequalities for a new data-based method for selecting nonparametric density estimates

Luc Devroye, Gabor Lugosi and Frederic Udina

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

Abstract: We continue the development of a method for the selection of a bandwidth or a number of design parameters in density estimation. We provide explicit non-asymptotic density-free inequalities that relate the $L_1$ error of the selected estimate with that of the best possible estimate, and study in particular the connection between the richness of the class of density estimates and the performance bound. For example, our method allows one to pick the bandwidth and kernel order in the kernel estimate simultaneously and still assure that for {\it all densities}, the $L_1$ error of the corresponding kernel estimate is not larger than about three times the error of the estimate with the optimal smoothing factor and kernel plus a constant times $\sqrt{\log n/n}$, where $n$ is the sample size, and the constant only depends on the complexity of the family of kernels used in the estimate. Further applications include multivariate kernel estimates, transformed kernel estimates, and variable kernel estimates.

Keywords: Density estimation; Kernel estimate; convergence; smoothing factor; minimum distance estimate; asymptotic optimality (search for similar items in EconPapers)
JEL-codes: C13 C14 (search for similar items in EconPapers)
Date: 1998-02
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://econ-papers.upf.edu/papers/281.pdf Whole Paper (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:281

Access Statistics for this paper

More papers in Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra
Bibliographic data for series maintained by ( this e-mail address is bad, please contact ).