PC Adjusted Testing for Low Dimensional Parameters
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916813229522944 |
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| author | Bhattacharya, Sohom Dey, Rounak Mukherjee, Rajarshi |
| author_facet | Bhattacharya, Sohom Dey, Rounak Mukherjee, Rajarshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_10774 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | PC Adjusted Testing for Low Dimensional Parameters Bhattacharya, Sohom Dey, Rounak Mukherjee, Rajarshi Statistics Theory Probability 62G10, 62G20, 62C20 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. |
| title | PC Adjusted Testing for Low Dimensional Parameters |
| topic | Statistics Theory Probability 62G10, 62G20, 62C20 |
| url | https://arxiv.org/abs/2209.10774 |