A flexible semiparametric regression model for bimodal, asymmetric and censored data

ABSTRACT

In this paper, we propose a new semiparametric heteroscedastic regression model allowing for positive and negative skewness and bimodal shapes using the B-spline basis for nonlinear effects. The proposed distribution is based on the generalized additive models for location, scale and shape framework in order to model any or all parameters of the distribution using parametric linear and/or nonparametric smooth functions of explanatory variables. We motivate the new model by means of Monte Carlo simulations, thus ignoring the skewness and bimodality of the random errors in semiparametric regression models, which may introduce biases on the parameter estimates and/or on the estimation of the associated variability measures. An iterative estimation process and some diagnostic methods are investigated. Applications to two real data sets are presented and the method is compared to the usual regression methods.

KEYWORDS:

• Censored data
• diagnostics
• P-splines
• regression models
• semiparamteric model

Acknowledgements

We are very grateful to a referee and an associate editor for helpful comments that improved the paper. We gratefully acknowledge financial support from CAPES and CNPq (Brazil).

Disclosure statement

No potential conflict of interest was reported by the author(s).