Composite Likelihood Methods Based on Minimum Density Power Divergence Estimator.

Elena Castilla,Leandro Pardo,Konstantinos Zografos,Nirian Martín

doi:10.3390/e20010018

Elena Castilla, Leandro Pardo + Show 2 more

Open Access

https://doi.org/10.3390/e20010018

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Abstract

In this paper, a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hypothesis is considered, and the robustness is studied on the basis of a simulation study. The composite minimum density power divergence estimator is also introduced, and its asymptotic properties are studied.

Highlights

It is well known that the likelihood function is one of the most important tools in classical inference, and the resultant estimator, the maximum likelihood estimator (MLE), has nice efficiency properties, it has not so good robustness properties.Tests based on MLE have, usually, good efficiency properties, but in the presence of outliers, the behavior is not so good
Many robust estimators have been introduced in the statistical literature, some of them based on distance measures or divergence measures
We focus on the definition and the study of Wald-type test statistics, which are defined by means of composite minimum density power divergence estimators (CMDPDE) estimators instead of minimum density power divergences estimators (MDPDE) estimators

Summary

Introduction

It is well known that the likelihood function is one of the most important tools in classical inference, and the resultant estimator, the maximum likelihood estimator (MLE), has nice efficiency properties, it has not so good robustness properties. Tests based on MLE (likelihood ratio test, Wald test, Rao’s test, etc.) have, usually, good efficiency properties, but in the presence of outliers, the behavior is not so good To solve these situations, many robust estimators have been introduced in the statistical literature, some of them based on distance measures or divergence measures. Have given good robust estimators: minimum density power divergences estimators (MDPDE) and, based on them, some robust test statistics have been considered for testing simple and composite null hypotheses. Some of these tests are based on divergence measures (see [2,3]), and some others are used to extend the classical Wald test; see [4,5,6] and the references therein.

Composite Minimum Density Power Divergence Estimator

Numerical Example

Findings

Conclusions