A uniform limit theorem for predictive distributions

Let be a filtration, {Xn} an adapted sequence of real random variables, and {[alpha]n} a predictable sequence of non-negative random variables with [alpha]1>0. Set and define the random distribution functions and . Under mild assumptions on {[alpha]n}, it is shown that , a.s. on the set {Fn or Bn convergesuniformly}. Moreover, conditions are given under which Fn converges uniformly with probability 1.

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Year of publication:	2002
Authors:	Berti, Patrizia ; Rigo, Pietro
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 56.2002, 2, p. 113-120
Publisher:	Elsevier
Keywords:	Almost sure uniform convergence Empirical distribution Predictive distribution

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005319637