Consistency of the kernel density estimator: a survey
نویسندگان
چکیده
منابع مشابه
Consistency of the kernel density estimator - a survey
Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions...
متن کاملConsistency of the kernel density estimator
Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions...
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Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infin...
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One of a nonparametric procedures used to estimate densities is kernel method. In this paper, in order to reduce bias of kernel density estimation, methods such as usual kernel(UK), geometric extrapolation usual kernel(GEUK), a bias reduction kernel(BRK) and a geometric extrapolation bias reduction kernel(GEBRK) are introduced. Theoretical properties, including the selection of smoothness para...
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ژورنال
عنوان ژورنال: Statistical Papers
سال: 2010
ISSN: 0932-5026,1613-9798
DOI: 10.1007/s00362-010-0338-1