Issue |
ESAIM: PS
Volume 8, August 2004
|
|
---|---|---|
Page(s) | 132 - 149 | |
DOI | https://doi.org/10.1051/ps:2004005 | |
Published online | 15 September 2004 |
Asymptotics for the Lp-deviation of the variance estimator under diffusion
1
Laboratoire de Statistiques LS-CREST,
ENSAE, 3 rue Pierre Larousse, France; doukhan@ensae.fr.
2
Universidad Central de Venezuela, Escuela de
Matemática,
Facultad de Ciencias,
AP. 47197, Los Chaguaramos Caracas 1041-A, Venezuela; jleon@euler.ciens.ucv.ve.
Received:
22
October
2002
Revised:
21
October
2003
We consider a diffusion process Xt smoothed with (small)
sampling parameter ε. As in Berzin, León and Ortega
(2001), we consider a kernel estimate
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
Mathematics Subject Classification: 60F05 / 60F25 / 60J60 / 60H05 / 62M02 / 62M05
Key words: Variance estimator / kernel / Lp-deviation / central limit theorem.
© EDP Sciences, SMAI, 2004
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