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.
| Original language | English |
|---|---|
| Pages (from-to) | 131-138 |
| Journal | Journal of Econometric Methods |
| Volume | 12 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2023 |
Keywords
- fixed effects model
- Helmert transformation
- panel data econometrics
- sample mean
- sample variance