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Asymptotics for the L p -deviation of the variance estimator under diffusion

Paul Doukhan;  José R. León — 2004

ESAIM: Probability and Statistics

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 h h ε p 2 α ^ ε - α p p - 𝔼 α ^ ε - α p p .

Asymptotics for the -deviation of the variance estimator under diffusion

Paul Doukhan;  José R. León — 2010

ESAIM: Probability and Statistics

We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate α ^ ε 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 1 h h ε p 2 α ^ ε - α p p - I E α ^ ε - α p p .

Dependent Lindeberg central limit theorem and some applications

Jean-Marc Bardet;  Paul Doukhan;  Gabriel Lang;  Nicolas Ragache — 2008

ESAIM: Probability and Statistics

In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the usual causal...

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