A Robust Quantile Regression Model for Count Data: The Half Cauchy Transformation Approach

This paper introduces an innovative approach to modelling count data through the introduction of a robust quantile regression model, the Half Cauchy Quantile Regression (HCQR). Count data is frequently challenged by outliers and skewed distributions. By integrating the heavy-tailed properties of the Half Cauchy distribution into the quantile regression framework, the HCQR model offers reliable estimates, particularly in the presence of extreme values. Quantile regression models, including HCQR, typically exhibit greater robustness to such extremes compared to traditional methods. The study highlights the limitations of traditional count regression models, such as the Negative Binomial Regression (NBR), particularly their performance inadequacies within the quantile regression framework. A comparative analysis using real-world crime data illustrates that the HCQR model substantially outperforms the NBR model. By integrating the half Cauchy distribution into the quantile regression framework, the HCQR model was formulated. In the Half Cauchy Quantile Regression Model, the Half Cauchy quantile function is used to transform the traditional quantile regression outputs, accommodating the characteristics of the Half Cauchy distribution. This superiority is demonstrated through improved metrics such as lower Standard Deviation, Skewness, Kurtosis, Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC), establishing HCQR's enhanced robustness and predictive accuracy.