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In this paper, a practical estimation method for a regression model isproposed using semiparametric efficient score functions applicable to data withvarious shapes of errors. First, I derive semiparametric efficient scorevectors for a homoscedastic regression model without any assumptions of errors.Next, the semiparametric efficient score function can be modified assuming acertain parametric distribution of errors according to the shape of the errordistribution or by estimating the error distribution non-parametrically.Nonparametric methods for errors can be used to estimate the parameters ofinterest or to find an appropriate parametric error distribution. In thisregard, the proposed estimation methods utilize both parametric andnonparametric methods for errors appropriately. Through numerical studies, theperformance of the proposed estimation methods is demonstrated.

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