The problems of estimation and detection of an infinitely-variate signal f observed in the continuous white noise model are studied. It is assumed that f belongs to a certain weighted tensor product space. Several examples of such a space are considered. Special attention is given to the tensor product space of analytic functions with exponential weights. In connection with estimating and detecting unknown signal, the problems of rate and sharp optimality are investigated. In particular, it is shown that the use of a weighted tensor product space makes it possible to avoid the "curse of dimensionality" phenomenon.

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Keywords multivariate functions, nonparametric estimation, nonparametric goodness-of-fit testing, weighted tensor product space, white noise model
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Journal Mathematical Methods of Statistics
Ingster, Y.I. (Yu I.), & Stepanova, N. (2009). Estimation and detection of functions from weighted tensor product spaces. Mathematical Methods of Statistics, 18(4), 310–340. doi:10.3103/S1066530709040024