Nonparametric sequential prediction for stationary processes

Morvai, Gusztáv; Weiss, Benjamin

Ann. Probab., Tome 39 (2011) no. 1, p. 1137-1160 / Harvested from Project Euclid

Résumé

We study the problem of finding an universal estimation scheme h_n : ℝⁿ→ℝ, n=1, 2, … which will satisfy ¶ lim_t→∞(1/t)∑_i=1^t|h_i(X₀, X₁, …, X_i−1)−E(X_i|X₀, X₁, …, X_i−1)|^p=0 a.s. ¶ for all real valued stationary and ergodic processes that are in L^p. We will construct a single such scheme for all 1+ L does.

Publié le : 2011-05-15
Classification: Nonparametric predicton, stationary processes, 60G45, 60G25, 62G05

@article{1300281735,
     author = {Morvai, Guszt\'av and Weiss, Benjamin},
     title = {Nonparametric sequential prediction for stationary processes},
     journal = {Ann. Probab.},
     volume = {39},
     number = {1},
     year = {2011},
     pages = { 1137-1160},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1300281735}
}

Morvai, Gusztáv; Weiss, Benjamin. Nonparametric sequential prediction for stationary processes. Ann. Probab., Tome 39 (2011) no. 1, pp.  1137-1160. http://gdmltest.u-ga.fr/item/1300281735/