2013
DOI: 10.1214/12-aop786
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Exchangeable sequences driven by an absolutely continuous random measure

Abstract: Let $S$ be a Polish space and $(X_n:n\geq1)$ an exchangeable sequence of $S$-valued random variables. Let $\alpha_n(\cdot)=P(X_{n+1}\in \cdot\mid X_1,\...,X_n)$ be the predictive measure and $\alpha$ a random probability measure on $S$ such that $\alpha_n\stackrel{\mathrm{weak}}{\longrightarrow}\alpha$ a.s. Two (related) problems are addressed. One is to give conditions for $\alpha\ll\lambda$ a.s., where $\lambda$ is a (nonrandom) $\sigma$-finite Borel measure on $S$. Such conditions should concern the finite … Show more

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Cited by 18 publications
(18 citation statements)
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“…The proof is based on a remarkable result in Berti et al . (), theorems 1 and 4, which shows that, for CID processes, the directing measure is absolutely continuous with respect to λ if and only if the predictive distribution is absolutely continuous and converges in total variation. This result does not apply directly to our setting, because ( θ n ) is not, generally, CID.…”
Section: A Statistical Interpretation Of Newton's Algorithmmentioning
confidence: 84%
See 1 more Smart Citation
“…The proof is based on a remarkable result in Berti et al . (), theorems 1 and 4, which shows that, for CID processes, the directing measure is absolutely continuous with respect to λ if and only if the predictive distribution is absolutely continuous and converges in total variation. This result does not apply directly to our setting, because ( θ n ) is not, generally, CID.…”
Section: A Statistical Interpretation Of Newton's Algorithmmentioning
confidence: 84%
“…In the on‐line appendix we provide two lemmas (lemmas A1.1 and A1.2), which are slight extensions of theorems 1 and 4 in Berti et al . (), the main difference being that we substitute the conditional identical distribution assumption with a martingale property that holds in our setting. These results lead to the following theorem.…”
Section: A Statistical Interpretation Of Newton's Algorithmmentioning
confidence: 99%
“…sequences have been introduced in [4] and [22] and then investigated in various papers; see e.g. [1], [2], [5], [6], [7], [8], [9], [11], [15], [18], [19].…”
Section: Conditional Identity In Distributionmentioning
confidence: 99%
“…sequences have been introduced in [4] and [22] and then investigated in various papers; see e.g. [1], [2], [5], [6], [7], [8], [9], [11], [14], [17], [18].…”
Section: Conditional Identity In Distributionmentioning
confidence: 99%