A PARAMETRIC BOOTSTRAP USING THE FIRST FOURMOMENTS OF THE RESIDUALS

We consider linear regression models and we suppose that disturbances are either Gaussian or non Gaussian. Until now, within the framework of the bootstrap, we thought that the error in rejection probability (ERP) had the same rate of convergence with the parametric bootstrap or the nonparametric bootstrap. For linear data generating processes (DGP) we show in this paper that this assertion is false if skewness and/or kurtosis coefficients of the distribution of the disturbances are nonnull. Indeed, we show that the ERP is the same for the asymptotic test as for the classical parametric bootstrap test it is based on. The only exception happens when we perform a t test or its associated bootstrap (parametric or not) in the model perform a t-test or its associated bootstrap test (parametric or not) in the linear regression model with only an intercept where the disturbances where the disturbances have nonnull kurtosis coefficient and a skewness coefficient equal to zero. In that case, the ERPs of any test we perform are of the same order. However, we provide a parametric bootstrap using the first four moments of the distribution of the residuals which is as accurate as a non parametric bootstrap which uses these first four moments implicitly. We will introduce it as the parametric bootstrap considering higher moments (CHM), and thus, we will speak about the parametric bootstrap CHM.