Appropriate use of parametric and nonparametric methods in estimating regression models with various shapes of errors

In this paper, a practical estimation method for a regression model is proposed using semiparametric efficient score functions applicable to data with various shapes of errors. First, I derive semiparametric efficient score vectors for a homoscedastic regression model without any assumptions of errors. Next, the semiparametric efficient score function can be modified assuming a specific parametric distribution of errors according to the shape of the error distribution or by estimating the error distribution nonparametrically. Nonparametric methods for errors can be used to estimate the parameters of interest or to find an appropriate parametric error distribution. In this regard, the proposed estimation methods utilize both parametric and nonparametric methods for errors appropriately. Through numerical studies, the performance of the proposed estimation methods is demonstrated.