A bootstrap test for exploring the impact of the covariates in the linear model with non-normal errors

Linear regression models have been extensively studied and used under the assumption that the model error term is normally distributed. However, in many practiced situations, this assumption may not be met. Thus, conclusions of statistical inference and hypothesis testing based on Ordinary Least Square (short for OLS) may be incorrect and unbelievable in condition of error term following non-normal distributions. Based on the above considerations, it is necessary for investigating linear regression models with non-normal errors. In this paper, we focus on the estimation and inference of the linear model with non-normal errors. Specifically, a non-parametric procedure is first developed for calibrating the model. Then, a bootstrap test is presented to detect the significance of the impact of certain covariates on the response based on the idea of variance analysis. Simulation results show that the estimation and proposed test method performs well.