Skip to main content

Advertisement

Nonparametric estimation of characteristics of the interspike interval distribution

Article metrics

  • 304 Accesses

We address the problem of non-parametric estimation of the probability density function as a description of the probability distribution of noncorrelated interspike intervals (ISI) in records of neuronal activity. We also continue our previous effort [1, 2] to propose alternative estimators of the variability measures. Kernel density estimators are probably the most frequently used non-parametric estimators of the probability distribution. However, there are also other non-parametric approaches. We focus on non-parametric methods based on a principle of extrema of the Fisher information. Specifically, we focus on the maximum penalized likelihood estimation of the probability density function proposed by Good and Gaskins [3], which can be understood as a kernel estimator with a particular kernel function [4]. Other non-parametric approach we would like to address is the spline interpolation proposed by Huber [5] which can uniquely estimate the ISI distribution.

References

  1. 1.

    Kostal L, Lansky P, Pokora O: Variability measures of positive random variables. PLoS ONE. 2011, 6: e21998-

  2. 2.

    Kostal L, Pokora O: Nonparametric Estimation of Information-Based Measures of Statistical Dispersion. Entropy. 2012, 14: 1221-1233.

  3. 3.

    Good IJ, Gaskins RA: Nonparametric roughness penalties for probability densities. Biometrika. 1971, 58: 255-277.

  4. 4.

    Eggermont PPB, LaRiccia VN: Maximum Penalized Likelihood Estimation: Volume I: Density Estimation. Springer. 2001

  5. 5.

    Huber PJ: Fisher information and spline interpolation. Ann. Stat. 1974, 2: 1029-1033.

Download references

Acknowledgements

This work was supported by the Czech Science Foundation (GACR) grants 15-06991S (Ondrej Pokora) and 15-08066S (Lubomir Kostal).

Author information

Correspondence to Ondrej Pokora.

Rights and permissions

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Keywords

  • Probability Density Function
  • Kernel Function
  • Kernel Density
  • Fisher Information
  • Density Estimator