论文标题
OLS估计量的渐近协方差矩阵的积极确定性在简约的回归中
Positive definiteness of the asymptotic covariance matrix of OLS estimators in parsimonious regressions
论文作者
论文摘要
最近，Ghysels，Hill和Motegi（2020）提出了一项测试，用于检查线性回归模型中大量系数是否为零。该测试称为最大测试。测试统计量是通过首先运行多个普通最小二乘（OLS）回归来计算的，每个回归仅包括一个关键回归器，其系数应在零下为零，然后进行这些关键回归器的平方OLS系数估计值的最大值。他们将这些回归称为简约的回归。本文回答了他们的言论2.4中提出的一个问题。在简约回归中，OLS估计量的渐近协方差矩阵是否通常是积极的。该论文表明它通常是正定的，并且可以利用结果来促进实现最大测试所需的模拟P值的计算。
Recently, Ghysels, Hill, and Motegi (2020) proposed a test for examining whether a large number of coefficients in linear regression models is zero. The test is called the max test. The test statistic is calculated by first running multiple ordinary least squares (OLS) regressions, each including only one of key regressors, whose coefficients are supposed to be zero under the null, and then taking the maximum value of the squared OLS coefficient estimates of those key regressors. They called these regressions parsimonious regressions. This paper answers a question raised in their Remark 2.4; whether the asymptotic covariance matrix of the OLS estimators in the parsimonious regressions is generally positive definite. The paper shows that it is generally positive definite, and the result may be utilized to facilitate the calculation of the simulated p value necessary for implementing the max test.
