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Estimating Functionals of a Stochastic Process

Part of: Design of experiments Numerical approximation and computational geometry Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Jacques Istas  and
Catherine Laredo
Jacques Istas*
Affiliation:
Institut National de la Recherche Agronomique
Catherine Laredo*
Affiliation:
Institut National de la Recherche Agronomique
*
∗ Postal address: Laboratoire de Biométrie, Domaine de Vilvert, I.N.R.A., 78350 Jouy-en-Josas, France.
∗ Postal address: Laboratoire de Biométrie, Domaine de Vilvert, I.N.R.A., 78350 Jouy-en-Josas, France.
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Abstract

The problem of estimating the integral of a stochastic process from observations at a finite number N of sampling points has been considered by various authors. Recently, Benhenni and Cambanis (1992) studied this problem for processes with mean 0 and Hölder index K + ½, K ; ℕ These results are here extended to processes with arbitrary Hölder index. The estimators built here are linear in the observations and do not require the a priori knowledge of the smoothness of the process. If the process satisfies a Hölder condition with index s in quadratic mean, we prove that the rate of convergence of the mean square error is N 2s+1 as N goes to ∞, and build estimators that achieve this rate.

Keywords

SECOND-ORDER PROCESSFUNCTIONALS ESTIMATIONDISCRETE SAMPLINGSMOOTH PROCESSWAVELETS

MSC classification

Primary: 60G12: General second-order processes 60G35: Signal detection and filtering 65D05: Interpolation
Secondary: 62K05: Optimal designs 62M99: None of the above, but in this section

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 1 , March 1997 , pp. 249 - 270
Copyright
Copyright © Applied Probability Trust 1997 

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