Rounak Dey | Searcharxiv

arXiv2025

PC Adjusted Testing for Low Dimensional Parameters

In this paper, we investigate the impact of high-dimensional Principal Component (PC) adjustments on inferring the effects of variables on outcomes, with a focus on applications in genetic association studies where PC adjustment is commonly used to account for population stratification. We consider high-dimensional linear regression in the regime where the number of covariates grows proportionally to the number of samples. In this setting, we provide an asymptotically precise understanding of when PC adjustments yield valid tests with controlled Type I error rates. Our results demonstrate that, under both fixed and diverging signal strengths, PC regression often fails to control the Type I error at the desired nominal level. Furthermore, we establish necessary and sufficient conditions for Type I error inflation based on covariate distributions. These theoretical findings are further supported by a series of numerical experiments.

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arXiv2016

Asymptotic properties of Principal Component Analysis and shrinkage-bias adjustment under the Generalized Spiked Population model

With the development of high-throughput technologies, principal component analysis (PCA) in the high-dimensional regime is of great interest. Most of the existing theoretical and methodological results for high-dimensional PCA are based on the spiked population model in which all the population eigenvalues are equal except for a few large ones. Due to the presence of local correlation among features, however, this assumption may not be satisfied in many real-world datasets. To address this issue, we investigated the asymptotic behaviors of PCA under the generalized spiked population model. Based on the theoretical results, we proposed a series of methods for the consistent estimation of population eigenvalues, angles between the sample and population eigenvectors, correlation coefficients between the sample and population principal component (PC) scores, and the shrinkage bias adjustment for the predicted PC scores. Using numerical experiments and real data examples from the genetics literature, we showed that our methods can greatly reduce bias and improve prediction accuracy.

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