A flexible Unit Chen quantile regression model for bounded response data: estimation, model diagnostics, and applications

Abstract

Bounded response variables are common in disciplines such as dependability, finance, environmental sciences, and biostatistics, where traditional regression models based on the conditional mean may fail to capture varied covariate effects throughout the response distribution. To solve this issue, this work proposes a flexible quantile regression model based on the Unit Chen distribution for evaluating continuous data on the unit intervals. The proposed methodology defines the conditional quantile via a logit link function, allowing explanatory factors to impact diverse parts of the answer distribution while maintaining limited support. Maximum likelihood estimation is created for the inference of parameters, and the appropriate estimation approach is executed by means of numerical optimization techniques. A number of model diagnostic techniques are included to check the adequacy and robustness of the model, to detect influential data and to examine the sensitivity of the fitted model, including generalized Cook’s distance, likelihood displacement and local influence analysis. The finite-sample performance of the suggested estimators is examined via a comprehensive Monte Carlo simulation analysis employing bias, mean squared error and root mean squared error as assessment measures for varying sample sizes and quantile levels. The practical applicability of the proposed model is illustrated using a real boundedresponse dataset and is compared with several competing unit quantile regression models using information criteria and diagnostic measures. The empirical findings demonstrate that the proposed Unit Chen quantile regression model provides accurate parameter estimation, effective diagnostic performance, and competitive model fitting, making it a valuable alternative for modeling bounded response data exhibiting heterogeneous distributional characteristics.