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Kernel Density Estimation for Random Symmetric Positive Definite Matrices

An R package with Wishart, log-Gaussian and Gaussian kernels for positive definite matrices, with optimal bandwidth selection based on least square cross validation or leave-one-out cross-validation criteria.

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Version

Install

install.packages('ksm')

Monthly Downloads

146

Version

1.0

License

MIT + file LICENSE

Maintainer

Leo Belzile

Last Published

October 28th, 2025

Functions in ksm (1.0)

lcv_kern_smlnorm

Likelihood cross validation criterion for symmetric matrix lognormal kernel

lcv_kern_Wishart

Likelihood cross validation criterion for Wishart kernel

lcv_kdens_symmat

Likelihood cross-validation for symmetric positive definite matrix kernels

Log of mean with precision

lscv_kern_Wishart

Least square cross validation criterion for Wishart kernel

Random vector generation from the multivariate normal distribution

Rotation matrix for 2 dimensional problems

Random matrix generation from first-order autoregressive Wishart process

Signed sum with precision

Random matrix generation from Wishart distribution

Log of sum with precision

Target densities for simulation study

Realized variance of Amazon and SPY

Random generation from first-order vector autoregressive model

simu_ise_montecarlo

Integrated squared error via Monte Carlo

Random matrix generation from matrix beta type II distribution

Random matrix generation from the inverse Wishart distribution

lcv_kern_smnorm

Likelihood cross validation criterion for symmetric matrix normal kernel

rotation_scaling

Rotation matrix with scaling for Monte Carlo integration

Symmetrize matrix

Rotation matrix for 3 dimensional problems

Target densities for simulation study

Kullback-Leibler divergence via Monte Carlo

bandwidth_optim

Bandwidth optimization for symmetric matrix kernels

Solver for Riccati equation

Density of Wishart random matrix

Symmetric matrix-variate lognormal density

Symmetric matrix-variate normal density

Matrix beta type II density function

Wishart kernel density

Symmetric matrix log-normal kernel density

Density of inverse Wishart random matrix

Integration with respect to symmetric positive definite matrices

lscv_kern_smlnorm

Least square cross validation criterion for log symmetric matrix normal kernel

Kernel density estimators for symmetric matrices

Symmetric matrix normal kernel density

Multivariate gamma function