Multivariate orthogonal series estimates for random design regression

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)$L_2({\mu }_n)$, where _μn${\mu }_n$ denotes the empirical design measure. The construction can be considered as designing adapted Haar wavelets.