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lp -deviation

ESAIM: Probability and Statistics (1)

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1 results

Asymptotics for the Lp -deviation of the variance estimator under diffusion
Paul Doukhan, José R. León
Journal:

ESAIM: Probability and Statistics / Volume 8 / August 2004

Published online by Cambridge University Press:

15 September 2004, pp. 132-149

Print publication:

August 2004
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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 $\widehat{\alpha}_{\varepsilon}$ with window h(ε) of afunction α of its variance. In order to exhibit globaltests of hypothesis, we derive here central limit theorems forthe Lp deviations such as \[ \frac1{\sqrt{h}}\left(\frac{h}\varepsilon\right)^{\frac{p}2}\left(\left\|\widehat{\alpha}_{\varepsilon}-{\alpha}\right\|_p^p-\mbox{I E}\left\|\widehat{\alpha}_{\varepsilon}-{\alpha}\right\|_p^p\right).\]