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Quasi‐universal bandwidth selection for kernel density estimators
Author(s) -
Wegkamp Marten H.
Publication year - 1999
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315649
Subject(s) - estimator , kernel density estimation , bandwidth (computing) , selection (genetic algorithm) , kernel (algebra) , mathematics , multivariate kernel density estimation , density estimation , construct (python library) , computer science , variable kernel density estimation , algorithm , statistics , kernel method , mathematical optimization , combinatorics , artificial intelligence , telecommunications , support vector machine , computer network
Let f̂ n , h denote the kernel density estimate based on a sample of size n drawn from an unknown density f. Using techniques from L 2 projection density estimators, the author shows how to construct a data‐driven estimator f̂ n , h which satisfies\documentclass{article}\pagestyle{empty}\begin{document}$$ \mathop {\sup }\limits_{{\rm bounded}} \mathop {\lim \;\sup }\limits_{n \to \infty } \frac{{\int {E|\hat f_{n,H} (x) - f(x)|^2 dx} }}{{\inf _{h > 0} \int {E|\hat f_{n,h} (x) - f(x)|^2 dx} }} = 1. $$\end{document}This paper is inspired by work of Stone (1984), Devroye and Lugosi (1996) and Birge and Massart (1997).