Max-sum tests for cross-sectional independence of high-dimensional panel data
高维面板数据截面独立性的最大值—求和检验AI 解读 ↓
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高维面板数据截面独立性的最大值—求和检验
- 研究问题
- 当面板截面单位数可能远大于观测数，且回归误差的截面相关性可能稀疏或非稀疏时，如何检验截面独立性？
- 方法与思路
- 作者研究基于残差相关性的求和、最大值及最大值—求和检验，并通过最大值与求和项的渐近独立性建立理论。
- 材料陈述的贡献
- 摘要称，文章解决相关系数平方和的两个猜想、建立最大值渐近理论，并用模拟和案例展示组合检验的功效及稳健性。
- 阅读关注点
- 应核对截面维度与时间维度的增长关系、误差和回归设计条件，以及组合检验的校准与不同稀疏情形下的比较。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；理论条件及具体模拟结果未提供，不能声称组合检验在所有情形均占优。
原文摘要
We consider a testing problem for cross-sectional independence for high-dimensional panel data, where the number of cross-sectional units is potentially much larger than the number of observations. The cross-sectional independence is described through linear regression models. We study three tests named the sum, the max and the max-sum tests, where the latter two are new. The sum test is initially proposed by Breusch and Pagan (1980). We design the max and sum tests for sparse and nonsparse correlation coefficients of random errors between the linear regression models, respectively. And the max-sum test is devised to compromise both situations on the correlation coefficients. Indeed, our simulation shows that the max-sum test outperforms the previous two tests. This makes the max-sum test very useful in practice where sparsity or not for a set of numbers is usually vague. Toward the theoretical analysis of the three tests, we have settled two conjectures regarding the sum of squares of sample correlation coefficients asked by Pesaran (2004 and 2008). In addition, we establish the asymptotic theory for maxima of sample correlation coefficients appeared in the linear regression model for panel data, which is also the first successful attempt to our knowledge. To study the max-sum test, we create a novel method to show asymptotic independence between maxima and sums of dependent random variables. We expect the method itself is useful for other problems of this nature. Finally, an extensive simulation study as well as a case study are carried out. They demonstrate advantages of our proposed methods in terms of both empirical powers and robustness for correlation coefficients of residuals regardless of sparsity or not.