On the Use of the Helmert Transformation, and its Applications in Panel Data Econometrics

Kolev Gueorgui I. () and Helmuts Azacis
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Kolev Gueorgui I.: Tilburg University, Tilburg, Netherlands

Journal of Econometric Methods, 2023, vol. 12, issue 1, 131-138

Abstract: We revisit the Helmert transformation, and provide a useful and simple derivation of the joint distribution of the sample mean and the sample variance in samples from independently and identically distributed normal random variables. Our derivation is distinguished by concreteness, very little abstractness, and should be appealing to beginning students of statistics, and to both beginning and advanced students of econometrics. We also highlight one fruitful application of the Helmert transformation in panel data econometrics. The Helmert transformation can be used to eliminate the fixed effects in the estimation of fixed effects models, and we briefly review this application of the transformation in the panel data context.

Keywords: Helmert transformation; sample mean; sample variance; panel data econometrics; fixed effects model (search for similar items in EconPapers)
JEL-codes: B23 C16 C20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/jem-2021-0023

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