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A faster algorithm to estimate multiresolution densities

Author

Listed:
  • Federico Palacios-González

    (University of Granada)

  • Rosa M. García-Fernández

    (University of Granada)

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.

Suggested Citation

  • Federico Palacios-González & Rosa M. García-Fernández, 2020. "A faster algorithm to estimate multiresolution densities," Computational Statistics, Springer, vol. 35(3), pages 1207-1230, September.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:3:d:10.1007_s00180-020-00952-w
    DOI: 10.1007/s00180-020-00952-w
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    References listed on IDEAS

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