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Estimation of integrated squared density derivatives from a contaminated sample

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Delaigle, Aurore [UCL] Gijbels, Irène [UCL]

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2002
Language Anglais
Journal information "Royal Statistical Society. Journal. Series B: Statistical Methodology" - Vol. 64, p. 869-886 (2002)
Peer reviewed yes
Publisher Blackwell Publ Ltd (Oxford)
issn 1369-7412
e-issn 1467-9868
Publication status Publié
Affiliation UCL - EUEN/STAT - Institut de statistique
Keywords characteristic function ; deconvolution ; errors in variables ; integrated squared derivatives ; kernel density estimation ; normal reference rule ; plug-in bandwidth selection
Links
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Bibliographic reference Delaigle, Aurore ; Gijbels, Irène. Estimation of integrated squared density derivatives from a contaminated sample. In: Royal Statistical Society. Journal. Series B: Statistical Methodology, Vol. 64, p. 869-886 (2002)
Permanent URL http://hdl.handle.net/2078.1/41540