Overview

This repository offers a user-friendly R package for an optimizer minimizing the density power divergence proposed by Basu et al. (1998) :

$$L_{\alpha}(\theta) = -\frac{1}{\alpha} \frac{1}{n} \sum_{i=1}^{n} f_{\theta}(z_i)^{\alpha} + \frac{1}{1+\alpha}\int f_{\theta}(z)^{1+\alpha} dz.$$

This optimizer needs minimal effort for users to obtain the optimal parameter, to estimate general parametric models. To cite this package, please cite the following manuscript:

@article{okuno2024DPD,
    year      = {2024},
    volume    = {},
    number    = {},
    pages     = {},
    author    = {Akifumi Okuno},
    title     = {Minimizing robust density power-based divergences for general parametric density models},
    journal   = {Annals of the Institute of Statistical Mathematics},
    note      = {To appear.}
}

Quickstart

Install

Please enter and execute the following command to install our sgdpd package.

install.packages("https://okuno.net/R-packages/sgdpd_1.0.0.zip", repos=NULL, type="win.binary")

Example

In order to showcase the capabilities of our optimizer, we perform a univariate skew-normal density estimation. Initially, we define the skew-normal density function, parameterized by theta. This is achieved using the dsnorm function, which is sourced from the fGarch package:

f <- function(z, theta) dsnorm(x=z, mean=theta[1], sd=theta[2], xi=theta[3])

Using the $n \times d$ design matrix Z, along with a specified learning rate lr, an initial parameter theta0, and an exponent parameter exponent, we can efficiently compute the optimal parameter as follows:

sgdpd(f=f, Z=Z, lr=0.1, theta0=c(0,1,1), exponent=0.2)

No further operation is needed! Please also see our user manual for more details.

Contact info.

• Akifumi Okuno (ISM and RIKEN AIP) https://okuno.net