Power Enhancement in High Dimensional Cross-Sectional Tests
高维截面检验的功效增强AI 解读 ↓
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高维截面检验的功效增强
- 研究问题
- 当高维零向量原假设仅被少数分量违反时，如何改善二次型检验对稀疏备择的低功效，同时保持可用的原假设分布？
- 方法与思路
- 作者通过筛选构造功效增强项，使其在原假设下以高概率为零、在稀疏备择下发散，再与渐近枢轴统计量相加。
- 材料陈述的贡献
- 摘要称组合检验可提高稀疏备择下的功效，其极限零分布由原枢轴统计量决定，增强项还可一致识别违反原假设的分量。
- 阅读关注点
- 应核对筛选阈值、增强项在原假设下消失的条件，以及因子定价检验和面板截面独立性检验中的具体实现与尺寸表现。
- 阅读边界
- 这是 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未列明正则条件与功效数值，不能据此认为适用于任意稀疏备择。
原文摘要
We propose a novel technique to boost the power of testing a high-dimensional vector $H:\btheta=0$ against sparse alternatives where the null hypothesis is violated only by a couple of components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due to the accumulation of errors in estimating high-dimensional parameters. More powerful tests for sparse alternatives such as thresholding and extreme-value tests, on the other hand, require either stringent conditions or bootstrap to derive the null distribution and often suffer from size distortions due to the slow convergence. Based on a screening technique, we introduce a "power enhancement component", which is zero under the null hypothesis with high probability, but diverges quickly under sparse alternatives. The proposed test statistic combines the power enhancement component with an asymptotically pivotal statistic, and strengthens the power under sparse alternatives. The null distribution does not require stringent regularity conditions, and is completely determined by that of the pivotal statistic. As a byproduct, the power enhancement component also consistently identifies the elements that violate the null hypothesis. As specific applications, the proposed methods are applied to testing the factor pricing models and validating the cross-sectional independence in panel data models.