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Multivariate orthogonal series estimates for random design regression
Authors:Michael Kohler
Institution:Department of Mathematics, Darmstadt University of Technology, Schlossgartenstrasse 7, D-64289 Darmstadt, Germany
Abstract:In this paper a new multivariate regression estimate is introduced. It is based on ideas derived in the context of wavelet estimates and is constructed by hard thresholding of estimates of coefficients of a series expansion of the regression function. Multivariate functions constructed analogously to the classical Haar wavelets are used for the series expansion. These functions are orthogonal in L2(μn)L2(μn), where μnμn denotes the empirical design measure. The construction can be considered as designing adapted Haar wavelets.
Keywords:primary  62G07  secondary  62G05
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