Finite exchangeability and linear regression

Marco Scarsini (1, 2) , Bruno Bassan

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 Dipartimento di Scienze Economiche e Aziendali

We consider a finite sequence of exchangeable binary random variables and assume that the conditional expected value of each variable is an average of the observed frequency of success and a prior guess. We obtain a representation of the law of the finite sequence as a beta-binomial. In this way we prove known results for infinite sequences by a simple passage to the limit. Our approach does not have the generality of the usual representation theorems for (finite or infinite) exchangeable sequences, but is very natural and is completely elementary.

Keywords: Exchangeability; Linear regression; Beta-binomial distribution; De Finetti's theorem

Domains: Humanities and Social Sciences; Economics and Finance; Economy and decision science

Marco Scarsini, Bruno Bassan. Finite exchangeability and linear regression. Statistics and Probability Letters, 1995, Vol. 23, N°2, pp. 105-110. ⟨10.1016/0167-7152(94)00100-M⟩. ⟨hal-00541806⟩