We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate with window of a function of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the deviations such as
Mots clés : variance estimator, kernel, $L^p$-deviation, central limit theorem
@article{PS_2004__8__132_0, author = {Doukhan, Paul and Le\'on, Jos\'e R.}, title = {Asymptotics for the $L^p$-deviation of the variance estimator under diffusion}, journal = {ESAIM: Probability and Statistics}, pages = {132--149}, publisher = {EDP-Sciences}, volume = {8}, year = {2004}, doi = {10.1051/ps:2004005}, mrnumber = {2085611}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2004005/} }
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 SP - 132 EP - 149 VL - 8 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2004005/ DO - 10.1051/ps:2004005 LA - en ID - PS_2004__8__132_0 ER -
%0 Journal Article %A Doukhan, Paul %A León, José R. %T Asymptotics for the $L^p$-deviation of the variance estimator under diffusion %J ESAIM: Probability and Statistics %D 2004 %P 132-149 %V 8 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2004005/ %R 10.1051/ps:2004005 %G en %F PS_2004__8__132_0
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/
[1] On the asymptotic normality of the -norm of empirical functional. Math. Methods Statist. 4 (1995) 1-19. | Zbl
and ,[2] Non-linear functionals of the Brownian bridge and some applications. Stoch. Proc. Appl. 92 (2001) 11-30. | Zbl
, and ,[3] Théorème de limite centrale pour un estimateur non paramétrique de la variance d'un processus de diffusion multidimensionnelle. Ann. Inst. Henri Poincaré, Probab. Stat. 29 (1993) 357-389. | Numdam | Zbl
,[4] The fast climate fluctuations during the stadial and interstadial climate states. Ann. Glaciology 35 (2002).
, and ,[5] Calcul de la vitesse de convergence dans le théorème central limite vis-à-vis des distances de Prohorov, Dudley et Lévy dans le cas de v. a. dépendantes. Probab. Math. Statist. 6 (1985) 19-27. | Zbl
, and ,[6] Non-parametric estimation of the diffusion coefficient by wavelets methods. Scand. J. Statist. 19 (1992) 317-335. | Zbl
, and ,[7] Stochastic differential equations. Springer-Verlag, Berlin, New York (1972). | MR | Zbl
and ,[8] The -norm density estimator process. To appear in Ann. Prob. | Zbl
, and ,[9] Parameter estimation for a discrete sampling of an integrated Ornstein-Uhlenbeck process. Statistics 35 (2000) 225-243. | Zbl
,[10] On continuous conditional martingales and stable convergence in law, sémin. Probab. XXXI, LNM 1655, Springer (1997) 232-246. | EuDML | Numdam | Zbl
,[11] Multiple Wiener-Itô integrals. Springer-Verlag, New York, Lect. Notes Math. 849 (1981). | MR | Zbl
,[12] Crossings and occupation measures for a class of semimartingales. Ann. Probab. 26 (1998) 253-266. | Zbl
and ,[13] Inference on the variance and smoothing of the paths of diffusions. Ann. Inst. Henri Poincaré, Probab. Stat. 38 (2002) 1009-1022. | EuDML | Numdam | Zbl
and ,[14] About the Lindeberg method for strongly mixing sequences. ESAIM: PS 1 (1995) 35-61. | EuDML | Numdam | Zbl
,[15] On the subspaces of , () spanned by sequences of independent random variables. Israël Jour. Math. 8 (1970) 273-303. | Zbl
,[16] On the convergence rate in the central limit theorem for -dependent random variables. Theor. Proba. Appl. 24 (1979) 782-796. | Zbl
,[17] Non-parametric estimation of the diffusion coefficient of a diffusion process. Stoch. Anal. Appl. 16 (1998) 185-200. | Zbl
,[18] Bilinear Stochastic Models and Related problems of Nonlinear Time Series. Springer-Verlag, New York, Lect. Notes Statist. 142 (1999). | MR | Zbl
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