Uniformly most powerful tests in linear models

Razvan G. Romanescu

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arXiv · 2411.18033

Uniformly most powerful tests in linear models

Razvan G. Romanescu

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Abstract

In the multiple regression model we prove that the coefficient t-test for a variable of interest is uniformly most powerful unbiased, with the other parameters considered nuisance. The proof is based on the theory of tests with Neyman-structure and does not assume unbiasedness or linearity of the test statistic. We further show that the Gram-Schmidt decomposition of the design matrix leads to a family of regression model with potentially more powerful tests for the corresponding transformed regressors. Finally, we discuss interpretation and performance criteria for the Gram-Schmidt regression compared to standard multiple regression, and show how the power differential has major implications for study design.

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Razvan G. Romanescu. 2024-11-27. Uniformly most powerful tests in linear models. https://arxiv.org/abs/2411.18033

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