# Power Enhancement in High Dimensional Cross-Sectional Tests

arXiv: https://arxiv.org/abs/1310.3899 · HTML: https://mlsanity.com/paper/1310.3899/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2013.

## Built on by (most cited first, 6 of 6)

- [Growing the Efficient Frontier on Panel Trees](https://mlsanity.com/paper/2501.16730/) (2025)
- [Forecast Evaluation in Large Cross-Sections of Realized Volatility](https://mlsanity.com/paper/2112.04887/) (2021)
- [Detection and Estimation of Structural Breaks in High-Dimensional Functional Time Series](https://mlsanity.com/paper/2304.07003/) (2023)
- [Group Shapley with Robust Significance Testing and Its Application to Bond Recovery Rate Prediction](https://mlsanity.com/paper/2501.03041/) (2025)
- [A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates](https://mlsanity.com/paper/2205.00171/) (2022)
- [A Unified Combination Framework for Dependent Tests with Applications to Microbiome Association Studies](https://mlsanity.com/paper/2404.09353/) (2024)

## Abstract (arXiv)

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.