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Estimation of integrated squared density derivatives from a contaminated sample
Author(s) -
Delaigle A.,
Gijbels I.
Publication year - 2002
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00366
Subject(s) - estimator , mean squared error , bandwidth (computing) , kernel density estimation , mathematics , statistics , variance (accounting) , bias of an estimator , kernel (algebra) , sample (material) , computer science , minimum variance unbiased estimator , discrete mathematics , chemistry , chromatography , computer network , accounting , business
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.