000184340 001__ 184340
000184340 005__ 20181203023014.0
000184340 0247_ $$2doi$$a10.1080/01621459.2012.695657
000184340 022__ $$a0162-1459
000184340 02470 $$2ISI$$a000309793400025
000184340 037__ $$aARTICLE
000184340 245__ $$aNonparametric Construction of Multivariate Kernels
000184340 260__ $$aAlexandria$$bAmerican Statistical Association$$c2012
000184340 269__ $$a2012
000184340 300__ $$a11
000184340 336__ $$aJournal Articles
000184340 520__ $$aWe propose a nonparametric method for constructing multivariate kernels tuned to the configuration of the sample, for density estimation in R-d, d moderate. The motivation behind the approach is to break down the construction of the kernel into two parts: determining its overall shape and then its global concentration. We consider a framework that is essentially nonparametric, as opposed to the usual bandwidth matrix parameterization. The shape of the kernel to be employed is determined by applying the backprojection operator, the dual of the Radon transform, to a collection of one-dimensional kernels, each optimally tuned to the concentration of the corresponding one-dimensional projections of the data. Once an overall shape is determined, the global concentration is controlled by a simple sealing. It is seen that the kernel estimators thus developed are easy and extremely fast to compute, and perform at least as well in practice as parametric kernels with cross-validated or otherwise tuned covariance structure. Connections with integral geometry are discussed, and the approach is illustrated under a wide range of scenarios in two and three dimensions, via an R package developed for its implementation.
000184340 6531_ $$aBackprojection
000184340 6531_ $$aBandwidth selection
000184340 6531_ $$aDensity estimation
000184340 6531_ $$aRadon transform
000184340 6531_ $$aSmoothing
000184340 700__ $$0243592$$aPanaretos, Victor M.$$g180565
000184340 700__ $$0243590$$aKonis, Kjell$$g182536
000184340 773__ $$j107$$k499$$q1085-1095$$tJournal Of The American Statistical Association
000184340 909C0 $$0252237$$pSMAT$$xU11798
000184340 909CO $$ooai:infoscience.tind.io:184340$$pSB$$particle
000184340 917Z8 $$x180122
000184340 937__ $$aEPFL-ARTICLE-184340
000184340 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000184340 980__ $$aARTICLE