具有非正态误差的线性模型的 Bootstrap 检验

线性回归模型已被广泛研究和使用，前提是模型误差项呈正态分布。但是，在许多实际情况下，此假设可能无法满足。如果模型误差项为非正态分布，则常用的最小二乘估计方法可能效率低下，从而导致无效的统计推断。因此，有必要研究具有非正态误差的线性模型的估计和推理。在本文中，我们重点介绍模型估计和协变量对响应的影响。具体来说，首先开发了一种非参数程序来校准模型。然后，提出了一个 bootstrap 检验，以基于方差分析的思想检测协变量影响的显着性。仿真结果表明，该估计和所提测试方法表现良好。

Linear regression models have been extensively studied and applied under the assumption that the model error terms follow a normal distribution. However, in many practical scenarios, this assumption may not hold. If the model error terms follow a non-normal distribution, the commonly used least squares estimation method may be inefficient, leading to invalid statistical inference. Therefore, it is necessary to investigate the estimation and inference of linear models with non-normal error terms. In this paper, we focus on model estimation and the effects of covariates on the response variable. Specifically, we first develop a nonparametric procedure for model calibration. Subsequently, we propose a bootstrap test to detect the significance of covariate effects based on the idea of analysis of variance (ANOVA). The simulation results demonstrate that the proposed estimation and test methods perform well.