Power Enhancement in High-Dimensional Cross-Sectional Tests

• 成果类型: Article
• 署名作者: Fan, Jianqing; Liao, Yuan; Yao, Jiawei
• 署名单位: Princeton University; Capital University of Economics & Business; Sun Yat Sen University; University System of Maryland; University of Maryland College Park
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA12749
• 发表日期: 2015
• 页码: 1497-1541
• 关键词: covariance-matrix estimation; LAGRANGE MULTIPLIER TEST; HIGHER CRITICISM; regularization; likelihood; arbitrage; number

摘要

We propose a novel technique to boost the power of testing a high-dimensional vector H:=0 against sparse alternatives where the null hypothesis is violated by only a few 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. The proposed methods are then applied to testing the factor pricing models and validating the cross-sectional independence in panel data models.