Off-diagonal elements of projection matrices and dimension asymptotics

Stanislav Anatolyev and Maksim Smirnov

Economics Letters, 2024, vol. 239, issue C

Abstract: We provide insights on asymptotic behavior of the off-diagonal elements of projection matrices in settings, where the dimension of underlying vectors grows with the sample size. Under designs favorable to application of the random matrix theory, the off-diagonal elements are asymptotically normal with a simple variance expression. We also discuss the robustness of the result to deviations of the design from the ideal setup.

Keywords: Projection matrix; Many instruments/regressors; Dimension asymptotics (search for similar items in EconPapers)
JEL-codes: C21 C26 C46 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:239:y:2024:i:c:s0165176524002453

DOI: 10.1016/j.econlet.2024.111761

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