ABSTRACT
The rôle of some wavelet methods in probability and statistics is illustrated via a sample of three problems: We show how properties of processes can be read from properties of their wavelet transform. We discuss how the missing data problem can be approached via frames of complex exponentials. We explain how wavelets can be used to span classes of admissible estimators in nonparametric function estimation. It is also the purpose of this paper to show that bridges can be crossed in the other directions: Random products of matrices determine the smoothness of compactly supported wavelets. Nonstationary prediction theory gives new results on frames in Hilbert space.
