A cross-validation approach to bandwidth selection for a kernel-based estimate of the density of a conditional expectation

To estimate the density f of a conditional expectation μ(Z) = E[X|Z], Steckley and Henderson (2003) sample independent copies Z 1 ,...,Z m ; then, conditional on Z i , they sample n independent samples of X, and their sample mean ̅X i is an approximate sample of μ(Z i ). For a kernel density estimat...

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Bibliographic Details
Main Author: Avramidis, A. N.
Format: Conference Proceeding
Language:English
Subjects:
Bandwidth
Convergence
Educational institutions
Estimation
Kernel
Mathematical model
Random variables
Online Access:Request full text
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Summary:To estimate the density f of a conditional expectation μ(Z) = E[X|Z], Steckley and Henderson (2003) sample independent copies Z 1 ,...,Z m ; then, conditional on Z i , they sample n independent samples of X, and their sample mean ̅X i is an approximate sample of μ(Z i ). For a kernel density estimate ̂f of f based on such samples and a bandwidth (smoothing parameter) h, they consider the mean integrated squared error (MISE), ∫(̂f(x)-f(x)) 2 dx, and find rates of convergence of m, n and h that optimize the rate of convergence of MISE to zero. Inspired by the cross-validation approach in classical density estimation, we develop an estimate of MISE (up to a constant) and select the h that minimizes this estimate. While a convergence analysis is lacking, numerical results suggest that our method is promising.
ISSN:0891-7736
1558-4305
DOI:10.1109/WSC.2011.6147771