3,391 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
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