Multivariate orthogonal series estimates for random design regression |
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Authors: | Michael Kohler |
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Institution: | Department of Mathematics, Darmstadt University of Technology, Schlossgartenstrasse 7, D-64289 Darmstadt, Germany |
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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), where μn denotes the empirical design measure. The construction can be considered as designing adapted Haar wavelets. |
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Keywords: | primary 62G07 secondary 62G05 |
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