A faster algorithm to estimate multiresolution densities

This paper develops a consistent estimator for coefficients of probability density functions defined in Multiresolution Analysis Structures ( MRD ), and an algorithm based on the proposed estimator. This algorithm, named FD , behaves similarly to the maximum likelihood estimator for large datasets. The process, by which the coefficients estimated by the FD algorithm and, then, used to estimate the MRD on a regular point grid, is called Multiresolution Density Estimation ( MRDE ) and leads to consistent MRD estimations. Simulations trials reveal that the FD algorithm based on a Frequency Data Count is faster and easier to apply than the Expectation Maximization ( EM ). The research also shows that using the same data and grid, the MRDE is frequently faster than the Kernel Density Estimation using Fast Fourier Transform algorithm $$(KDE_{FFT})$$ ( K D E FFT ) . These results suggest the MRDE method for estimating Multiresolution densities could be applied to estimate probability densities in the big data field.

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