Asymptotics for the L p -deviation of the variance estimator under diffusion
ESAIM: Probability and Statistics, Tome 8 (2004), pp. 132-149.

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 hh ε p 2 α ^ ε -α p p -𝔼α ^ ε -α p p .

DOI : 10.1051/ps:2004005
Classification : 60F05, 60F25, 60J60, 60H05, 62M02, 62M05
Mots clés : variance estimator, kernel, $L^p$-deviation, central limit theorem
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     title = {Asymptotics for the $L^p$-deviation of the variance estimator under diffusion},
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     pages = {132--149},
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     url = {http://www.numdam.org/articles/10.1051/ps:2004005/}
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Doukhan, Paul; León, José R. Asymptotics for the $L^p$-deviation of the variance estimator under diffusion. ESAIM: Probability and Statistics, Tome 8 (2004), pp. 132-149. doi : 10.1051/ps:2004005. http://www.numdam.org/articles/10.1051/ps:2004005/

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