Asymptotics for the L p -deviation of the variance estimator under diffusion
ESAIM: Probability and Statistics, Volume 8  (2004), p. 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 : https://doi.org/10.1051/ps:2004005
Classification:  60F05,  60F25,  60J60,  60H05,  62M02,  62M05
Keywords: 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},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2004},
     pages = {132-149},
     doi = {10.1051/ps:2004005},
     zbl = {pre02161879},
     mrnumber = {2085611},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 8 (2004) , pp. 132-149. doi : 10.1051/ps:2004005. http://www.numdam.org/item/PS_2004__8__132_0/

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