# Estimaci\'on de la inicial de referencia utilizando simulaci\'on

## TL;DR

This paper analyzes and improves a simulation-based method for estimating reference priors, focusing on estimator consistency, variance reduction, and asymptotic interval estimation.

## Contribution

It derives the estimator's variance, constructs probability intervals, and explores variance reduction techniques to enhance estimation accuracy and efficiency.

## Key findings

- Variance of the estimator was derived and used for interval estimation.
- Variance reduction via common random numbers significantly improved precision.
- In some cases, the estimator's error was eliminated using the variance reduction technique.

## Abstract

The method proposed by Bernardo and Smith [2000] to approximate reference priors by simulation was analyzed with the objective of improving the procedure in order to obtain consistent estimators and to allow the estimation of asymptotic probability intervals. In this sense, the variance of Bernardo's estimator was derived and was used to construct probability intervals that permitted the expression of the estimation error as a function of sample size. Additionally a variance reduction technique (common random numbers) were explored as a means to obtain more precise estimations with smaller sample sizes. These technique was found to considerably reduce estimation error for some of the examples explored. In other cases the use of the technique resulted in zero estimation error given that the estimator does not depend on the sample.

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Source: https://tomesphere.com/paper/1704.01932