Cauchy-Aggregated Ridge Tests for High-Dimensional Factor Pricing Models
Abstract
In high-dimensional factor pricing models, the power of regularized alpha tests depends on the ridge parameter, whose optimal value varies with the unknown direction of pricing errors. We address this tuning uncertainty by combining ridge-specific p-values using the Cauchy rule. The resulting test retains the least-squares alpha estimator and residual sample covariance and accommodates more assets than observations. We establish the joint Gaussian limits of the component statistics under the null and local alternatives and derive an explicit covariance formula across ridge parameters. These results characterize the combined test's asymptotic distribution and local power and justify its tail calibration. Simulations show empirical rejection rates close to the nominal levels and power gains over the fixed-ridge benchmark, with power approaching that of signal-informed ridge benchmarks across the simulated settings.
Related
- Central limit theorems for high-dimensional ridge regression under uniform subsampling
- Infinite-Dimensional Spherical Kernel ridge Regression
- Adaptable High-Dimensional Change Point Detection via Ridge Regularization
- A Pricing and Hedging Framework for Infinite-Dimensional Financial Markets
- Holomorphic Cauchy Networks for Efficient Stationary Tail Computation in High-Dimensional Reflected Brownian Motions
BibTeX
@misc{zhao2026cauchyaggregated,
title = {{Cauchy-Aggregated Ridge Tests for High-Dimensional Factor Pricing Models}},
author = {Ping Zhao and Dan Zhuang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06112},
eprint = {2610.06112},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06112},
}
RIS
TY - UNPB
TI - Cauchy-Aggregated Ridge Tests for High-Dimensional Factor Pricing Models
AU - Ping Zhao
AU - Dan Zhuang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06112
UR - https://arxiv.org/abs/2610.06112
AB - In high-dimensional factor pricing models, the power of regularized alpha tests depends on the ridge parameter, whose optimal value varies with the unknown direction of pricing errors. We address this tuning uncertainty by combining ridge-specific p-values using the Cauchy rule. The resulting test retains the least-squares alpha estimator and residual sample covariance and accommodates more assets than observations. We establish the joint Gaussian limits of the component statistics under the null and local alternatives and derive an explicit covariance formula across ridge parameters. These results characterize the combined test's asymptotic distribution and local power and justify its tail calibration. Simulations show empirical rejection rates close to the nominal levels and power gains over the fixed-ridge benchmark, with power approaching that of signal-informed ridge benchmarks across the simulated settings.
ER -