Let $x=(x_n:n \in N)$ be a sequence of random variables with values in a Polish space X. If x is exchangeable (stationary), then x is i.i.d. (ergodic) conditionally on some random probability measure p on B(x) (q on B($X^\infty$). In the exchangeable case, two necessary and sufficient conditions are given for x to be i.i.d. conditionally on t(p), where t is a given transformation. Essentially the same conditions apply when x is stationary, apart from "i.i.d." is replaced by "ergodic" and p by q. The basic difference between the exchangeable and the stationary case lies in the empirical measure to be used. Up to a proper choice of the latter, the two conditions work in a large class of invariant distributions for x. Finally, the set of ergodic probability measures is shown to be a Borel set, and almost sure weak convergence of a certain sequence of empirical measures is proved in the stationary case.

On parametric models for invariant probability measures / Berti, Patrizia; Fortini, S.; Ladelli, L.; Regazzini, E.; Rigo, P.. - In: QUADERNI DI STATISTICA. - ISSN 1594-3739. - STAMPA. - 2:(2000), pp. 39-57.

On parametric models for invariant probability measures

BERTI, Patrizia;
2000

Abstract

Let $x=(x_n:n \in N)$ be a sequence of random variables with values in a Polish space X. If x is exchangeable (stationary), then x is i.i.d. (ergodic) conditionally on some random probability measure p on B(x) (q on B($X^\infty$). In the exchangeable case, two necessary and sufficient conditions are given for x to be i.i.d. conditionally on t(p), where t is a given transformation. Essentially the same conditions apply when x is stationary, apart from "i.i.d." is replaced by "ergodic" and p by q. The basic difference between the exchangeable and the stationary case lies in the empirical measure to be used. Up to a proper choice of the latter, the two conditions work in a large class of invariant distributions for x. Finally, the set of ergodic probability measures is shown to be a Borel set, and almost sure weak convergence of a certain sequence of empirical measures is proved in the stationary case.
2
39
57
On parametric models for invariant probability measures / Berti, Patrizia; Fortini, S.; Ladelli, L.; Regazzini, E.; Rigo, P.. - In: QUADERNI DI STATISTICA. - ISSN 1594-3739. - STAMPA. - 2:(2000), pp. 39-57.
Berti, Patrizia; Fortini, S.; Ladelli, L.; Regazzini, E.; Rigo, P.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/449226
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact