Let (Xn) be a sequence of random variables, adapted to a filtration (Gn), and let (Formula Presented) be the empirical and the predictive measures. We focus on (Formula Presented) where D is a class of measurable sets. Conditions for (Formula Presented), almost surely or in probability, are given. Also, to determine the rate of convergence, the asymptotic behavior of rn||μn-an|| is investigated for suitable constants rn. Special attention is paid to rn = √n and (Formula Presented). The sequence (Xn) is exchangeable or, more generally, conditionally identically distributed.
Asymptotic predictive inference with exchangeable data / Berti, Patrizia; Pratelli, Luca; RIGO, PIETRO. - In: REVISTA BRASILEIRA DE PROBABILIDADE E ESTATÍSTICA. - ISSN 0103-0752. - STAMPA. - 32:4(2018), pp. 815-833. [10.1214/17-BJPS367]
Asymptotic predictive inference with exchangeable data
RIGO, PIETRO
2018
Abstract
Let (Xn) be a sequence of random variables, adapted to a filtration (Gn), and let (Formula Presented) be the empirical and the predictive measures. We focus on (Formula Presented) where D is a class of measurable sets. Conditions for (Formula Presented), almost surely or in probability, are given. Also, to determine the rate of convergence, the asymptotic behavior of rn||μn-an|| is investigated for suitable constants rn. Special attention is paid to rn = √n and (Formula Presented). The sequence (Xn) is exchangeable or, more generally, conditionally identically distributed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.