Robust Procedures for Estimating and Testing in the Framework of Divergence Measures.

The approach for estimating and testing based on divergence measures has become, in the last 30 years, a very popular technique not only in the field of statistics, but also in other areas, such as machine learning, pattern recognition, etc [...

Model Selection in a Composite Likelihood Framework Based on Density Power Divergence.

This paper presents a model selection criterion in a composite likelihood framework based on density power divergence measures and in the composite minimum density power divergence estimators, which depends on an tuning parameter α . After introducing such a criterion, some asymptotic properties are established. We present a simulation study and two numerical examples in order to point out the robustness properties of the introduced model selection criterion.

A New Class of Robust Two-Sample Wald-Type Tests.

Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for testing such two sample problems using the minimum density power divergence estimators of the underlying parameters. In particular, we consider the simple two-sample hypothesis concerning the full parametric homogeneity as well as the general two-sample (composite) hypotheses involving some nuisance parameters.

New robust statistical procedures for the polytomous logistic regression models.

This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis.

Composite Likelihood Methods Based on Minimum Density Power Divergence Estimator.

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.

Using Cook's distance in polytomous logistic regression.

The previously unknown asymptotic distribution of Cook's distance in polytomous logistic regression is established as a linear combination of independent chi-square random variables with one degree of freedom. An exhaustive approach to the analysis of influential covariates is developed and a new measure for the accuracy of predictions based on such a distribution is provided. Two examples with real data sets (one with continuous covariates and the other with both qualitative and quantitative covariates) are presented to illustrate the approach developed.

A New Class of Minimum Power Divergence Estimators with Applications to Cancer Surveillance.

The Annual Percent Change (APC) has been adopted as a useful measure for analyzing the changing trends of cancer mortality and incidence rates by the NCI SEER program. Difficulties, however, arise when comparing the sample APCs between two overlapping regions because of the induced dependence (e.g.

Multiple comparison of trends in cancer rates taking into account overlapping cases().

When analyzing trends in cancer rates, it is common to rely on the so-called Annual Percent Change (APC). For dealing with such a measure of trend, directly age-adjusted rates are usually considered. Classical methods such as pooled t-tests are often applied for comparing APCs of two groups of individuals in a simple way under independence assumption.

Homogeneity/heterogeneity hypotheses for standardized mortality ratios based on minimum power-divergence estimators.

This paper analyzes the power divergence estimators when homogeneity/heterogeneity hypotheses among standardized mortality ratios (SMRs) are taken into account. A Monte Carlo study shows that when the standard mortality rate is not external, that is it is estimated from the sample data, these estimators have a good performance even for small sample sets and in particular the minimum chi-square estimators have a better behavior compared to the classical maximum likelihood estimators. In order to make decisions under homogeneity/heterogeneity hypotheses of SMRs we propose some test-statistics which consider the minimum power divergence estimators.