Asymptotics for the Lp-deviation of the variance estimator under diffusion

Paul Doukhan; José R. León

ESAIM: Probability and Statistics (2010)

  • Volume: 8, page 132-149
  • ISSN: 1292-8100

Abstract

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We consider a diffusion process Xt smoothed with (small) sampling parameter ε. As in Berzin, León and Ortega (2001), we consider a kernel estimate α ^ ε with window h(ε) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the Lp deviations such as 1 h h ε p 2 α ^ ε - α p p - I E α ^ ε - α p p .

How to cite

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Doukhan, Paul, and León, José R.. "Asymptotics for the Lp-deviation of the variance estimator under diffusion." ESAIM: Probability and Statistics 8 (2010): 132-149. <http://eudml.org/doc/104315>.

@article{Doukhan2010,
abstract = { We consider a diffusion process Xt smoothed with (small) sampling parameter ε. As in Berzin, León and Ortega (2001), we consider a kernel estimate $\widehat\{\alpha\}_\{\varepsilon\}$ with window h(ε) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the Lp deviations such as \[ \frac1\{\sqrt\{h\}\}\left(\frac\{h\}\varepsilon\right)^\{\frac\{p\}2\}\left( \left\|\widehat\{\alpha\}\_\{\varepsilon\}-\{\alpha\}\right\|\_p^p- \mbox\{I E\}\left\|\widehat\{\alpha\}\_\{\varepsilon\}-\{\alpha\}\right\|\_p^p \right). \]},
author = {Doukhan, Paul, León, José R.},
journal = {ESAIM: Probability and Statistics},
keywords = {Variance estimator; kernel; Lp-deviation; central limit theorem.; -deviation; central limit theorem},
language = {eng},
month = {3},
pages = {132-149},
publisher = {EDP Sciences},
title = {Asymptotics for the Lp-deviation of the variance estimator under diffusion},
url = {http://eudml.org/doc/104315},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Doukhan, Paul
AU - León, José R.
TI - Asymptotics for the Lp-deviation of the variance estimator under diffusion
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 132
EP - 149
AB - We consider a diffusion process Xt smoothed with (small) sampling parameter ε. As in Berzin, León and Ortega (2001), we consider a kernel estimate $\widehat{\alpha}_{\varepsilon}$ with window h(ε) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the Lp deviations such as \[ \frac1{\sqrt{h}}\left(\frac{h}\varepsilon\right)^{\frac{p}2}\left( \left\|\widehat{\alpha}_{\varepsilon}-{\alpha}\right\|_p^p- \mbox{I E}\left\|\widehat{\alpha}_{\varepsilon}-{\alpha}\right\|_p^p \right). \]
LA - eng
KW - Variance estimator; kernel; Lp-deviation; central limit theorem.; -deviation; central limit theorem
UR - http://eudml.org/doc/104315
ER -

References

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