Estimation of integrated squared density derivatives from a contaminated sample

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2002 · Volume 64 · Issue 4

Abstract

Summary.We propose a kernel estimator of integrated squared density derivatives, from a sample that has been contaminated by random noise. We derive asymptotic expressions for the bias and the variance of the estimator and show that the squared bias term dominates the variance term. This coincides with results that are available for non-contaminated observations. We then discuss the selection of the bandwidth parameter when estimating integrated squared density derivatives based on contaminated data. We propose a data-driven bandwidth selection procedure of the plug-in type and investigate its finite sample performance via a simulation study.

Keywords

Characteristic function, Deconvolution, Errors in variables, Integrated squared derivatives, Kernel density estimation, Normal reference rule, Plug-in bandwidth selection

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