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Nonparametric estimation of characteristics of the interspike interval distribution
BMC Neuroscience volume 16, Article number: P131 (2015)
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 , which can be understood as a kernel estimator with a particular kernel function . Other non-parametric approach we would like to address is the spline interpolation proposed by Huber  which can uniquely estimate the ISI distribution.
Kostal L, Lansky P, Pokora O: Variability measures of positive random variables. PLoS ONE. 2011, 6: e21998-
Kostal L, Pokora O: Nonparametric Estimation of Information-Based Measures of Statistical Dispersion. Entropy. 2012, 14: 1221-1233.
Good IJ, Gaskins RA: Nonparametric roughness penalties for probability densities. Biometrika. 1971, 58: 255-277.
Eggermont PPB, LaRiccia VN: Maximum Penalized Likelihood Estimation: Volume I: Density Estimation. Springer. 2001
Huber PJ: Fisher information and spline interpolation. Ann. Stat. 1974, 2: 1029-1033.
This work was supported by the Czech Science Foundation (GACR) grants 15-06991S (Ondrej Pokora) and 15-08066S (Lubomir Kostal).