355 research outputs found
Nonparametric sequential prediction for stationary processes
We study the problem of finding an universal estimation scheme
, which will satisfy
\lim_{t\rightarrow\infty}{\frac{1}{t}}\sum_{i=1}^t|h_
i(X_0,X_1,...,X_{i-1})-E(X_i|X_0,X_1,...,X_{i-1})|^p=0 a.s. for all real valued
stationary and ergodic processes that are in . We will construct a single
such scheme for all , and show that for mere integrability
does not suffice but does.Comment: Published in at http://dx.doi.org/10.1214/10-AOP576 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
On universal estimates for binary renewal processes
A binary renewal process is a stochastic process taking values in
where the lengths of the runs of 1's between successive zeros are
independent. After observing one would like to predict the
future behavior, and the problem of universal estimators is to do so without
any prior knowledge of the distribution. We prove a variety of results of this
type, including universal estimates for the expected time to renewal as well as
estimates for the conditional distribution of the time to renewal. Some of our
results require a moment condition on the time to renewal and we show by an
explicit construction how some moment condition is necessary.Comment: Published in at http://dx.doi.org/10.1214/07-AAP512 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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