Regularized Parametric Modal Regression: Lasso, Elastic Net and Ridge

Variable selection and estimation for parametric modal regression with continuous positive responses (Gamma, Weibull and Lognormal families) under Lasso, elastic-net, ridge and adaptive-Lasso penalties. The conditional mode is linked to a linear predictor through a logarithmic link using the mode reparameterization of Galarza and Lachos (2026) . The penalized log-likelihood is maximized with a proximal Newton algorithm (iteratively reweighted penalized least squares): at each iteration the modal log-likelihood is replaced by a local quadratic surrogate in the linear predictor, which yields a pseudo-response and a working weight in closed form, and the resulting weighted penalized least-squares subproblem is solved by the coordinate-descent solver of 'glmnet' (Friedman, Hastie and Tibshirani, 2010, ). The regularization parameter is chosen along a warm-started path by the extended Bayesian information criterion of Chen and Chen (2008) .