Asymptotics for the L p -deviation of the variance estimator under diffusion

Paul Doukhan; José R. León

ESAIM: Probability and Statistics (2004)

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

Abstract

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We consider a diffusion process X t 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 L p deviations such as 1 h h ε p 2 α ^ ε - α p p - 𝔼 α ^ ε - α p p .

How to cite

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Doukhan, Paul, and León, José R.. "Asymptotics for the $L^p$-deviation of the variance estimator under diffusion." ESAIM: Probability and Statistics 8 (2004): 132-149. <http://eudml.org/doc/245384>.

@article{Doukhan2004,
abstract = {We consider a diffusion process $X_t$ smoothed with (small) sampling parameter $\varepsilon $. As in Berzin, León and Ortega (2001), we consider a kernel estimate $\widehat\{\alpha \}_\{\varepsilon \}$ with window $h(\varepsilon )$ of a function $\alpha $ of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the $L^p$ deviations such as\[\hspace*\{-28.45274pt\} \frac\{1\}\{\sqrt\{h\}\}\left(\frac\{h\}\{\varepsilon \}\right)^\{\frac\{p\}\{2\}\}\left( \left\Vert \widehat\{\alpha \}\_\{\varepsilon \}-\{\alpha \}\right\Vert \_p^p- \mathbb \{E\}\left\Vert \widehat\{\alpha \}\_\{\varepsilon \}-\{\alpha \}\right\Vert \_p^p \right). \]},
author = {Doukhan, Paul, León, José R.},
journal = {ESAIM: Probability and Statistics},
keywords = {variance estimator; kernel; $L^p$-deviation; central limit theorem; Variance estimator; -deviation},
language = {eng},
pages = {132-149},
publisher = {EDP-Sciences},
title = {Asymptotics for the $L^p$-deviation of the variance estimator under diffusion},
url = {http://eudml.org/doc/245384},
volume = {8},
year = {2004},
}

TY - JOUR
AU - Doukhan, Paul
AU - León, José R.
TI - Asymptotics for the $L^p$-deviation of the variance estimator under diffusion
JO - ESAIM: Probability and Statistics
PY - 2004
PB - EDP-Sciences
VL - 8
SP - 132
EP - 149
AB - We consider a diffusion process $X_t$ smoothed with (small) sampling parameter $\varepsilon $. As in Berzin, León and Ortega (2001), we consider a kernel estimate $\widehat{\alpha }_{\varepsilon }$ with window $h(\varepsilon )$ of a function $\alpha $ of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the $L^p$ deviations such as\[\hspace*{-28.45274pt} \frac{1}{\sqrt{h}}\left(\frac{h}{\varepsilon }\right)^{\frac{p}{2}}\left( \left\Vert \widehat{\alpha }_{\varepsilon }-{\alpha }\right\Vert _p^p- \mathbb {E}\left\Vert \widehat{\alpha }_{\varepsilon }-{\alpha }\right\Vert _p^p \right). \]
LA - eng
KW - variance estimator; kernel; $L^p$-deviation; central limit theorem; Variance estimator; -deviation
UR - http://eudml.org/doc/245384
ER -

References

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