Some New Robust Estimators for Circular Logistic Regression Model with Applications on Meteorological and Ecological Data

Abstract

Maximum likelihood estimation ( $\text{MLE}$ ) is often used to estimate the parameters of the circular logistic regression model due to its efficiency under a parametric model. However, evidence has shown that the classical $\text{MLE}$ extremely affects the parameter estimation in the presence of outliers. This article discusses the effect of outliers on circular logistic regression and extends four robust estimators, namely, Mallows, Schweppe, Bianco and Yohai estimator $\left(\text{BY}\right)$ , and weighted $\text{BY}$ estimators, to the circular logistic regression model. These estimators have been successfully used in linear logistic regression models for the same purpose. The four proposed robust estimators are compared with the classical $\text{MLE}$ through simulation studies. They demonstrate satisfactory finite sample performance in the presence of misclassified errors and leverage points. Meteorological and ecological datasets are analyzed for illustration.