Robust Estimation in Generalised Linear Models : The Density Power Divergence Approach

Abstract

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may not be linear or the distributions may not be normal in all the cases. However, quite often such real data contain a significant number of outliers in relation to the standard parametric model used in the analysis; in such cases the classical maximum likelihood estimator may fail to produce reasonable estimators and related inference could be unreliable. In this paper, we develop a robust estimation procedure for the generalised linear models that can generate robust estimators with little loss in efficiency. We will also explore two particular cases of the generalised linear model in details -- Poisson regression for count data and logistic regression for binary data -- which are widely applied in real life experiments. We will also illustrate the performance of the proposed estimators through several interesting data examples

Pre-print, 22 pages

Cited by in corpus (15)

• Influence Analysis of Robust Wald-type Tests
• A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator
• Robust Inference under the Beta Regression Model with Application to Health Care Studies
• New robust statistical procedures for polytomous logistic regression models
• Robust Wald-type tests for non-homogeneous observations based on minimum density power divergence estimator
• Ultrahigh-dimensional Robust and Efficient Sparse Regression using Non-Concave Penalized Density Power Divergence
• The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach
• On Difference Between Two Types of $\gamma$-divergence for Regression
• Robust and Efficient Parameter Estimation based on Censored Data with Stochastic Covariates
• Robust Estimation under Linear Mixed Models: The Minimum Density Power Divergence Approach
• Robust Rayleigh Regression Method for SAR Image Processing in Presence of Outliers
• On the Properties of Simulation-based Estimators in High Dimensions
• Robust mislabel logistic regression without modeling mislabel probabilities
• Robust Wald-type test in GLM with random design based on minimum density power divergence estimators
• Power and Level Robustness of A Composite Hypothesis Testing under Independent Non-Homogeneous Data