ore
15:30
presso Vitali
Abstract:
<br />
Almost all work on empirical processes, so far,
<br />
concerned i.i.d.
<br />
data. To my knowledge, the non independent case is almost neglected and
<br />
essentially
<br />
restricted to ergodic sequences. In this talk, convergence in distribution
<br />
(under uniform distance) of empirical processes, based on non ergodic data,
<br />
is investigated. I focus on
<br />
conditionally identically distributed sequences of
<br />
random variables. This type of dependence, more general than
<br />
exchangeability, plays a role in
<br />
Bayesian predictive inference. Some foundational problems, connected to
<br />
convergence in distribution of non measurable random elements, are also
<br />
discussed. Among other things, necessary and sufficient conditions for
<br />
convergence in distribution of empirical processes for exchangeable data
<br />
are given.