sshist: Optimal Density Estimation via Shimazaki-Shinomoto Method

The sshist package implements state-of-the-art algorithms for optimal non-parametric density estimation based on the framework developed by Hideaki Shimazaki and Shigeru Shinomoto (2007, 2010). The core optimization principle is to find the parameters that minimize the expected Mean Integrated Squared Error (MISE) between the estimated density and the true, unknown underlying distribution.

By utilizing purely data-driven optimization, this package avoids subjective choices for bin widths or kernel bandwidths, making it highly robust—especially for data with complex, multimodal, or heavy-tailed structures.

Key Features

Data-Driven Optimization: Replaces subjective “rules of thumb” (like Sturges’ or Freedman-Diaconis’ rules) with objective minimizers of the MISE cost function.
Multi-Dimensional Support: Provides full capability for both 1D univariate and 2D bivariate distributions.
Fixed and Variable Estimators: Offers both classical global estimators and advanced locally adaptive variable bandwidth selectors (based on Abramson’s scaling method).
High Performance: Designed to evaluate cost functions efficiently, leveraging analytical formulations and fast backend calculations.

Summary of Available Functions

Function	Estimator Type	Dimension	Bandwidth / Bin Selection
`sshist`	Histogram	1D	Fixed (single optimal bin width)
`sshist_2d`	Histogram	2D	Fixed independent bin width per axis
`sskernel`	Kernel Density	1D	Fixed global bandwidth
`ssvkernel`	Kernel Density	1D	Locally adaptive variable bandwidth
`sskernel2d`	Kernel Density	2D	Fixed global isotropic bandwidth
`ssvkernel2d`	Kernel Density	2D	Locally adaptive bivariate bandwidth

Installation

You can install the stable version of sshist from CRAN:

install.packages("sshist")

Alternatively, you can install the development version directly from GitHub using devtools:

# install.packages("devtools")
devtools::install_github("celebithil/sshist")

References

Shimazaki, H. and Shinomoto, S. (2007). A method for selecting the bin size of a time histogram. Neural Computation, 19(6), 1503–1527. doi:10.1162/neco.2007.19.6.1503
Shimazaki, H. and Shinomoto, S. (2010). Kernel bandwidth optimization in spike rate estimation. Journal of Computational Neuroscience, 29(1-2), 171–182. doi:10.1007/s10827-009-0180-4
https://www.neuralengine.org/res/histogram.html
https://github.com/shimazaki/density_estimation
https://s-shinomoto.com/toolbox/sshist/hist.html