Power Enhancement in High-Dimensional Cross-Sectional Tests
提出一种筛选技术增强高维向量零假设检验的功效，在稀疏备择下快速发散，结合渐近枢轴统计量确定零分布，应用于因子定价模型和面板数据截面独立性检验。
We propose a novel technique to boost the power of testing a high-dimensional vector <i>H</i> : <b><i>θ</i></b> = 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 specific applications, the proposed methods are applied to testing the factor pricing models and validating the cross-sectional independence in panel data models.