When are the Mean and the Studentized Differences Independent?

Bondesson, Lennart

Ann. Statist., Tome 4 (1976) no. 1, p. 668-672 / Harvested from Project Euclid

Résumé

Let $X_1, \cdots, X_n$ be i.i.d. rv's. Let further $\bar{X} = \sum X_i/n, S^2 = \sum(X_i - \bar{X})^2$, and $U = ((X_1 - \bar{X})/S, \cdots, (X_n - \bar{X})/S)$. If the variables $X_i$ are normally distributed or distributed as linearly transformed Gamma variables, $\bar{X}$ and $U$ are independent. In this paper we show that also the converse must hold.

Publié le : 1976-05-14
Classification: Constant regression, Cauchy's functional equation, characteristic function, analytic function, 62E10

@article{1176343477,
     author = {Bondesson, Lennart},
     title = {When are the Mean and the Studentized Differences Independent?},
     journal = {Ann. Statist.},
     volume = {4},
     number = {1},
     year = {1976},
     pages = { 668-672},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176343477}
}

Bondesson, Lennart. When are the Mean and the Studentized Differences Independent?. Ann. Statist., Tome 4 (1976) no. 1, pp.  668-672. http://gdmltest.u-ga.fr/item/1176343477/