Power Enhancement in High-Dimensional Cross-Sectional Tests

2015/01/01 by Jianqing Fan, Yuan Liao, Jiawei Yao · 412 citations
Economics, Econometrics and Finance · Mathematics · #Alternative hypothesis #Applied mathematics #Artificial intelligence #Computer science #Convergence (economics) #Data mining #Independence (probability theory) #Mathematical optimization #Mathematics #Null (SQL) #Null distribution #Null hypothesis #Quadratic equation #Spatial and Panel Data Analysis #Statistic #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical hypothesis testing #Statistics #Test statistic #Thresholding #Wald test

paper · doi:10.3982/ecta12749

published in Econometrica 83(4), 1497-1541 (Wiley)

openalex publication_date 2015/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

= 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.

Cited by

• Max-sum tests for cross-sectional independence of high-dimensional panel data
• Asymptotically independent U-statistics in high-dimensional testing
• Joint limiting laws for high-dimensional independence tests
• Financial inclusion and economic growth: The role of non-bank financial intermediation
• Escaping the Regional Carbon Trap: The Role of Renewable Energy Innovation in EU Decarbonisation
• Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors
• Uniform Inference for Characteristic Effects of Large Continuous-Time Linear Models
• Do Governments React to Public Debt Accumulation? A Cross-Country Analysis
• Paving the way for sustainable green growth in G10 economies: Perspectives on green manufacturing employment and renewable energy employment
• Bootstrapping ℓ_p-Statistics in High Dimensions
• High-Dimensional Hettmansperger-Randles Estimator and its Applications
• Upholding the green agenda of COP27 through publicly funded R&D on energy efficiencies, renewables, nuclear and power storage technologies
• Power Enhancement in High Dimensional Cross-Sectional Tests. [europepmc]
• An adaptive two-sample test for high-dimensional means. [europepmc]
• Testing for Marginal Linear Effects in Quantile Regression. [europepmc]
• An improved statistical model for taxonomic assignment of metagenomics. [europepmc]
• Homogeneity tests of covariance matrices with high-dimensional longitudinal data. [europepmc]
• Statistical inference of genetic pathway analysis in high dimensions. [europepmc]
• ASYMPTOTICALLY INDEPENDENT U-STATISTICS IN HIGH-DIMENSIONAL TESTING. [europepmc]
• Change-Point Detection in a High-Dimensional Multinomial Sequence Based on Mutual Information. [europepmc]
• Linear Hypothesis Testing in Linear Models With High-Dimensional Responses. [europepmc]
• Power-enhanced two-sample mean tests for high-dimensional microbiome compositional data. [europepmc]
• Obesity Kuznets Curve conjecture assessment in African economies: conditioning effects of urbanization, food, and trade using gender-based regional analysis. [europepmc]
• A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates. [europepmc]
• A Novel Approach of High Dimensional Linear Hypothesis Testing Problem. [europepmc]
• Socio-structural determinants of burn injuries in Africa: The role of social inequality, informal housing, and access to clean cooking energy technology. [europepmc]
• Testing the Graph of a Gaussian Graphical Model [europepmc]

Related

• Power Enhancement in High Dimensional Cross-Sectional Tests
• Unified and robust Lagrange multiplier type tests for cross-sectional independence in large panel data models
• Consistent complete independence test in high dimensions based on Chatterjee correlation coefficient
• Power in High-Dimensional Testing Problems
• Enhanced power enhancements for testing many moment equalities: Beyond the 2- and ∞-norm