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Asymptotics for the Lp-deviation of the variance estimator under diffusion
Published online by Cambridge University Press: 15 September 2004
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 \[ \frac1{\sqrt{h}}\left(\frac{h}\varepsilon\right)^{\frac{p}2}\left( \left\|\widehat{\alpha}_{\varepsilon}-{\alpha}\right\|_p^p- \mbox{I E}\left\|\widehat{\alpha}_{\varepsilon}-{\alpha}\right\|_p^p \right). \]
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- Research Article
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- © EDP Sciences, SMAI, 2004
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