论文标题
在特殊相对论下的线性回归
Linear Regression under Special Relativity
论文作者
论文摘要
这项研究调查了通过使用普通最小二乘（OLS）在特殊相对论的特定背景下估算简单线性回归的参数所带来的问题，其中独立变量仅限于开放间隔（-c，c）。发现在Lorentz速度转换下，斜率系数的OLS估计值并不不变。因此，提出了在特殊相对论下线性回归参数的替代估计量。在特殊相对论下，该估计量可以视为OLS估计量的概括。当C接近无穷大时，提出的估计量及其方差分别收敛到OLS估计器及其方差。所提出的估计值的方差大于OLS估计量的差异，这意味着使用OLS估计量进行假设检验及其方差可能会导致在特殊相对论下进行自由检验。
This study investigated the problem posed by using ordinary least squares (OLS) to estimate parameters of simple linear regression under a specific context of special relativity, where an independent variable is restricted to an open interval, (-c, c). It is found that the OLS estimate for the slope coefficient is not invariant under Lorentz velocity transformation. Accordingly, an alternative estimator for the parameters of linear regression under special relativity is proposed. This estimator can be considered a generalization of the OLS estimator under special relativity; when c approaches to infinity, the proposed estimator and its variance converges to the OLS estimator and its variance, respectively. The variance of the proposed estimator is larger than that of the OLS estimator, which implies that hypothesis testing using the OLS estimator and its variance may result in a liberal test under special relativity.
