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dc.contributor.authorSchick, Anton
dc.contributor.authorWefelmeyer, Wolfgang
dc.date.accessioned2008-03-20T12:00:16Z
dc.date.accessioned2016-10-05T14:14:07Z
dc.date.available2008-03-20T12:00:16Z
dc.date.available2016-10-05T14:14:07Z
dc.date.issued2008-03-11
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1125
dc.descriptionResearch in Pairs 2007en_US
dc.description.abstractIt has been shown recently that, under an appropriate integrability condition, densities of functions of independent and identically distributed random variables can be estimated at the parametric rate by a local U-statistic, and a functional central limit theorem holds. For the sum of two squared random variables, the integrability condition typically fails. We show that then the estimator behaves differently for different arguments. At points in the support of the squared random variable, the rate of the estimator slows down by a logarithmic factor and is independent of the bandwidth, but the asymptotic variance depends on the rate of the bandwidth, and otherwise only on the density of the squared random variable at this point and at zero. A functional central limit theorem cannot hold. Of course, for bounded random variables, the sum of squares is more spread out than a single square. At points outside the support of the squared random variable, the estimator behaves classically. Now the rate is again parametric, the asymptotic variance has a different form and does not depend on the bandwidth, and a functional central limit theorem holds.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2008,07
dc.subjectconvolution density estimatoren_US
dc.subjectsmoothness of convolutionsen_US
dc.subjectasymptotically linear estimatoren_US
dc.titleNon-Standard Behavior of Density Estimators for Sums of Squared Observationsen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2008-07
local.scientificprogramResearch in Pairs 2007
local.series.idOWP-2008-07
local.subject.msc62


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