Estimating the conditional expectations for continuous time stationary processes

Gusztáv Morvai; Benjamin Weiss

Kybernetika (2020)

  • Volume: 56, Issue: 3, page 410-431
  • ISSN: 0023-5954

Abstract

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One of the basic estimation problems for continuous time stationary processes X t , is that of estimating E { X t + β | X s : s ∈ [ 0 , t ] } based on the observation of the single block { X s : s ∈ [ 0 , t ] } when the actual distribution of the process is not known. We will give fairly optimal universal estimates of this type that correspond to the optimal results in the case of discrete time processes.

How to cite

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Morvai, Gusztáv, and Weiss, Benjamin. "Estimating the conditional expectations for continuous time stationary processes." Kybernetika 56.3 (2020): 410-431. <http://eudml.org/doc/297050>.

@article{Morvai2020,
abstract = {One of the basic estimation problems for continuous time stationary processes $X_t$, is that of estimating $E\lbrace X_\{t+\beta \}| X_s : s \in [0, t]\rbrace $ based on the observation of the single block $\lbrace X_s : s \in [0, t]\rbrace $ when the actual distribution of the process is not known. We will give fairly optimal universal estimates of this type that correspond to the optimal results in the case of discrete time processes.},
author = {Morvai, Gusztáv, Weiss, Benjamin},
journal = {Kybernetika},
keywords = {nonparametric estimation; continuous time stationary processes},
language = {eng},
number = {3},
pages = {410-431},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Estimating the conditional expectations for continuous time stationary processes},
url = {http://eudml.org/doc/297050},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Morvai, Gusztáv
AU - Weiss, Benjamin
TI - Estimating the conditional expectations for continuous time stationary processes
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 3
SP - 410
EP - 431
AB - One of the basic estimation problems for continuous time stationary processes $X_t$, is that of estimating $E\lbrace X_{t+\beta }| X_s : s \in [0, t]\rbrace $ based on the observation of the single block $\lbrace X_s : s \in [0, t]\rbrace $ when the actual distribution of the process is not known. We will give fairly optimal universal estimates of this type that correspond to the optimal results in the case of discrete time processes.
LA - eng
KW - nonparametric estimation; continuous time stationary processes
UR - http://eudml.org/doc/297050
ER -

References

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