Density estimation from streaming data using wavelets

In this paper we discuss approaches to estimating probability densities from streaming data based on wavelets. It is expected that streaming datasets are large and that the rate of data acquisition is very high. Thus it is not possible to recompute the entire density so that recursive algorithms are necessary. In addition, because streaming data are typically not stationary, older data in the stream are usually less valuable. It is, therefore, necessary to discount older data. We develop in this paper a methodology that is applicable to any orthonormal bases, but, in particular, a methodology for wavelet bases.