A faster algorithm to estimate multiresolution densities

Federico Palacios-González () and Rosa M. García-Fernández ()
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Federico Palacios-González: University of Granada
Rosa M. García-Fernández: University of Granada

Computational Statistics, 2020, vol. 35, issue 3, No 12, 1207-1230

Abstract: Abstract 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.

Keywords: MRA; Density estimation; Cubic Box Spline; Big-data; FD algorithm (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00180-020-00952-w

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