Rate of convergence of predictive distributions for dependent data
نویسندگان
چکیده
منابع مشابه
Rate of Convergence of Predictive Distributions for Dependent Data
This paper deals with empirical processes of the type Cn(B) = √ n ̆ μn(B) − P (Xn+1 ∈ B | X1, . . . , Xn) ̄ , where (Xn) is a sequence of random variables and μn = (1/n) P n i=1 δXi the empirical measure. Conditions for supB |Cn(B)| to converge stably (in particular, in distribution) are given, where B ranges over a suitable class of measurable sets. These conditions apply when (Xn) is exchangeab...
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Convergence rate for predictive recursion estimation of finite mixtures
Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models. It is known that the PR estimates of both the mixing and mixture densities are consistent under fairly mild conditions, but currently very little is known about the rate of convergence. In this note we investigate asymptotic convergence properties of the PR estimate u...
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2009
ISSN: 1350-7265
DOI: 10.3150/09-bej191