Power Enhancement in High Dimensional Cross-Sectional Tests.

Area of Science:

• Statistics
• Econometrics

Background:

• High-dimensional data analysis presents challenges for traditional statistical tests.
• Existing methods for sparse alternatives (e.g., Wald, thresholding, extreme-value tests) have limitations in power, require stringent conditions, or suffer from size distortions.

Purpose of the Study:

• To propose a novel technique for boosting the power of hypothesis testing against sparse alternatives in high-dimensional settings.
• To address the limitations of existing quadratic form tests and sparse alternative tests.

Main Methods:

• Introduced a screening technique to develop a "power enhancement component" that is zero under null hypothesis but diverges under sparse alternatives.
• Combined this component with an asymptotically pivotal statistic to create a new test statistic.
• The null distribution is determined by the pivotal statistic without stringent regularity conditions.

Main Results:

• The proposed test statistic strengthens power under sparse alternatives.
• The method avoids the low power issues of quadratic forms and the convergence/distortion problems of other sparse tests.
• Demonstrated applicability to testing factor pricing models and validating cross-sectional independence in panel data.

Conclusions:

• The novel technique effectively enhances statistical test power for high-dimensional sparse alternatives.
• The method offers a robust and more accurate approach compared to existing techniques.
• The approach has practical applications in econometrics and panel data analysis.