# retel

## Overview

retel implements the regularized exponentially tilted empirical likelihood method. The proposed method removes the convex hull constraint using a novel regularization technique, providing a suitable pseudo-likelihood for Bayesian inference.

The following functions enable users to set estimating functions by providing data and parameters:

`etel()`

computes exponentially tilted empirical likelihood without regularization.
`retel()`

computes regularized exponentially tilted empirical likelihood with regularization parameters.

This repository accompanies the research paper titled ‘Regularized Exponentially Tilted Empirical Likelihood for Bayesian Inference,’ available on arXiv. The `retel-paper`

folder contains code and additional resources related to the paper. This work was supported by the U.S. National Science Foundation under Grants No. SES-1921523 and DMS-2015552.

## Installation

You can install the latest stable release of retel from CRAN.

### Development version

You can install the development version of retel from GitHub.

## Usage

```
library(retel)
# Generate data
set.seed(63456)
x <- rnorm(100)
# Define an estimating function (ex. mean)
fn <- function(x, par) {
x - par
}
# Set parameter value
par <- 0
# Set regularization parameters
mu <- 0
Sigma <- 1
tau <- 1
# Call the retel function to compute the log-likelihood ratio. The return value
# contains the optimization results as the attribute 'optim'.
retel(fn, x, par, mu, Sigma, tau)
#> [1] -0.06709306
#> attr(,"optim")
#>
#> Call:
#>
#> nloptr(x0 = rep(0, p), eval_f = eval_obj_fn, eval_grad_f = eval_gr_obj_fn,
#> opts = opts, g = g, mu = mu, Sigma = Sigma, n = n, tau = tau)
#>
#>
#> Minimization using NLopt version 2.7.1
#>
#> NLopt solver status: 1 ( NLOPT_SUCCESS: Generic success return value. )
#>
#> Number of Iterations....: 4
#> Termination conditions: xtol_rel: 1e-04
#> Number of inequality constraints: 0
#> Number of equality constraints: 0
#> Optimal value of objective function: 0.999330716387232
#> Optimal value of controls: -0.03738174
```