Selection of the Blur Coefficient for Probability Density Kernel Estimates Under Conditions of Large Samples

  • A. V. LapkoEmail author
  • V. A. Lapko

A fast algorithm is proposed for choosing the blur factors of kernel functions of a non-parametric probability density estimate under conditions of large-scale statistical data. It is shown that the basis of the algorithm is the result of a study of the asymptotic properties of a new kernel probability density estimate. The properties of the developed algorithm are analyzed and the method of its application is formulated.


kernel probability density estimate quick selection of blur factors discretization of the range of values of a random variable large volume statistical data 


  1. 1.
    A. V. Lapko and V. A. Lapko, Multilevel Nonparametric Information Processing Systems, Sib-GAU, Krasnoyarsk (2013).Google Scholar
  2. 2.
    A. V. Lapko and V. A. Lapko, “Regression estimation of multidimensional probability density and its properties,” Avtometriya, 50, No. 2, 50–56 (2014).Google Scholar
  3. 3.
    M. I. Borrajo, W. González-Manteiga, and M. D. Martínez-Miranda, “Bandwidth selection for kernel density estimation with length-biased data,” J. Nonparam. Stat., 29, No. 3, 636–668 (2017).MathSciNetCrossRefGoogle Scholar
  4. 4.
    S. Chen, “Optimal bandwidth selection for kernel density functionals estimation,” J. Probab. Stat., 2015, 1–21 (2015), DOI: Scholar
  5. 5.
    D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, John Wiley & Sons, New Jersey (2015).Google Scholar
  6. 6.
    S. J. Sheather, “Density estimation,” Stat. Sci., 19, No. 4, 588–597 (2004).CrossRefGoogle Scholar
  7. 7.
    B. W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London (1986).Google Scholar
  8. 8.
    A. V. Lapko and V. A. Lapko, “A fast algorithm for choosing kernel function blur coefficients in a nonparametric probability density estimate,” Izmer. Tekhn., No. 6, 16–20 (2018), DOI: 10.32446/0368-1025it.2018-6-16-20.Google Scholar
  9. 9.
    A. V. Lapko and V. A. Lapko, “A fast algorithm for choosing blur ratios in multidimensional kernel estimates of probability density,” Izmer. Tekhn., No. 10, 19–23 (2018), DOI: 10.32446/0368-1025it.2018-10-19-23.Google Scholar
  10. 10.
    A. V. Lapko and V. A. Lapko, “Optimal choice of the number of discretization intervals of the domain of variation of a one-dimensional random variable when estimating the probability density,” Izmer. Tekhn., No. 7, 24–27 (2013).Google Scholar
  11. 11.
    V. A. Epanechnikov, “Nonparametric estimation of multidimensional probability density,” Teor. Veroyatn. Primen.,14, No. 1, 156–161 (1969).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Computational ModelingSiberian Branch of the Russian Academy of SciencesKrasnoyarskRussia
  2. 2.Reshetnev Siberian State University of Science and TechnologyKrasnoyarskRussia

Personalised recommendations