Advances in Modal Regression: From Theoretical Foundations to Practical Implementations

Modal regression has emerged as a powerful alternative to traditional mean and quantile regression by focusing on estimating the conditional mode rather than the conditional mean or quantiles. This approach offers robustness to outliers and skewed distributions while providing more informative prediction intervals for heterogeneous data. Recent advances span parametric, semiparametric, and nonparametric methods, with applications ranging from econometrics and finance to public health and biostatistics. This review systematically synthesizes theoretical developments, computational algorithms, and practical implementations of modal regression, highlighting its advantages in robust estimation and predictive modeling. Key challenges and future directions are discussed to guide further research in this evolving field. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical Models > Semiparametric Models