TY - JOUR
T1 - ON sequential estimation and prediction for discrete time series
AU - Morvai, Gusztáv
AU - Weiss, Benjamin
PY - 2007/12
Y1 - 2007/12
N2 - The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process X0, X1,...,Xn has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for P(Xn+1 X0, X1,...,Xn) can be found which converges to the true estimator almost surely. Despite this result, for restricted classes of processes, or for sequences of estimators along stopping times, universal estimators can be found. We present here a survey of some of the recent work that has been done along these lines.
AB - The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process X0, X1,...,Xn has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for P(Xn+1 X0, X1,...,Xn) can be found which converges to the true estimator almost surely. Despite this result, for restricted classes of processes, or for sequences of estimators along stopping times, universal estimators can be found. We present here a survey of some of the recent work that has been done along these lines.
KW - Nonparametric estimation
KW - Stationary processes
UR - http://www.scopus.com/inward/record.url?scp=38049125792&partnerID=8YFLogxK
U2 - 10.1142/S021949370700213X
DO - 10.1142/S021949370700213X
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AN - SCOPUS:38049125792
SN - 0219-4937
VL - 7
SP - 417
EP - 437
JO - Stochastics and Dynamics
JF - Stochastics and Dynamics
IS - 4
ER -