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We propose a new semiparametric regression model with exponentiated power exponential errors using the B-spline basis for nonlinear effects. We adopt the framework of the generalized additive models for location, scale, and shape to fit this regression model. We obtain the maximum penalized likelihood estimates of the model parameters by considering nonlinear effects. Some global-influence measurements and quantile residuals are also investigated. Various Monte Carlo simulations are performed for inference purposes under different parameter settings, systematic components and sample sizes. The proposals are illustrated by two applications to real data.

The exponentiated power exponential semiparametric regression model