# Minimax results for estimating integrals of analytic processes

ESAIM: Probability and Statistics (2010)

- Volume: 2, page 109-121
- ISSN: 1292-8100

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topBenhenni, Karim, and Istas, Jacques. "Minimax results for estimating integrals of analytic processes ." ESAIM: Probability and Statistics 2 (2010): 109-121. <http://eudml.org/doc/116582>.

@article{Benhenni2010,

abstract = {
The problem of predicting integrals of stochastic processes is
considered. Linear estimators have been constructed by means of
samples at N discrete times for processes having a fixed
Hölderian regularity s > 0 in quadratic mean. It is known
that the rate of convergence of the mean squared error is of
order N-(2s+1). In the class of analytic processes
Hp, p ≥ 1, we show that among all estimators,
the linear ones are optimal. Moreover, using optimal coefficient
estimators derived through the inversion of the covariance matrix,
the corresponding maximal error has lower and upper bounds with
exponential rates. Optimal simple nonparametric estimators with
optimal sampling designs are constructed in H² and
H∞ and have also bounds with exponential rates.
},

author = {Benhenni, Karim, Istas, Jacques},

journal = {ESAIM: Probability and Statistics},

keywords = {Integral prediction / analytic process / Hardy space /
Blaschke products. ; integrals of stochastic processes; analytic processes; linear estimators},

language = {eng},

month = {3},

pages = {109-121},

publisher = {EDP Sciences},

title = {Minimax results for estimating integrals of analytic processes },

url = {http://eudml.org/doc/116582},

volume = {2},

year = {2010},

}

TY - JOUR

AU - Benhenni, Karim

AU - Istas, Jacques

TI - Minimax results for estimating integrals of analytic processes

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 2

SP - 109

EP - 121

AB -
The problem of predicting integrals of stochastic processes is
considered. Linear estimators have been constructed by means of
samples at N discrete times for processes having a fixed
Hölderian regularity s > 0 in quadratic mean. It is known
that the rate of convergence of the mean squared error is of
order N-(2s+1). In the class of analytic processes
Hp, p ≥ 1, we show that among all estimators,
the linear ones are optimal. Moreover, using optimal coefficient
estimators derived through the inversion of the covariance matrix,
the corresponding maximal error has lower and upper bounds with
exponential rates. Optimal simple nonparametric estimators with
optimal sampling designs are constructed in H² and
H∞ and have also bounds with exponential rates.

LA - eng

KW - Integral prediction / analytic process / Hardy space /
Blaschke products. ; integrals of stochastic processes; analytic processes; linear estimators

UR - http://eudml.org/doc/116582

ER -

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