Doukhan, Paul; Jakubowicz, Jérémie; León, José Rafael Variance estimation with applications. (English) Zbl 1310.62043 Berkes, István (ed.) et al., Dependence in probability, analysis and number theory. A volume in memory of Walter Philipp. Most papers based on the presentations at the conference, Graz, Austria, June 17–20, 2009. Heber City, UT: Kendrick Press (ISBN 0-9793183-8-6/pbk). 203-231 (2010). Summary: Self-normalized central limit theorems are important for statistical purposes. A simple way to achieve them is to consider estimations of the limit variance; this expression writes as a complicated covariance series under weak dependence. Using an argument of E. Carlstein [Ann. Stat. 14, 1171–1179 (1986; Zbl 0602.62029)], we work out this program for a new procedure, in the case of vector valued stationary sequences \(\lambda\)-weakly dependent, introduced by P. Doukhan and S. Louhichi [Stochastic Processes Appl. 84, No. 2, 313–342 (1999; Zbl 0996.60020)], rich in examples. Our estimator admits a limiting variance which is useful for technical purpose. Applications to linear models with dependent inputs, sea waves modelling and stochastic differential equations exhibit explicit examples for which such procedures will be proved to be useful through simulation studies.For the entire collection see [Zbl 1196.60010]. Cited in 3 Documents MSC: 62G05 Nonparametric estimation 60F05 Central limit and other weak theorems 62G20 Asymptotic properties of nonparametric inference Keywords:variance estimation; weak dependence. Citations:Zbl 0602.62029; Zbl 0996.60020 PDFBibTeX XMLCite \textit{P. Doukhan} et al., in: Dependence in probability, analysis and number theory. A volume in memory of Walter Philipp. Most papers based on the presentations at the conference, Graz, Austria, June 17--20, 2009. Heber City, UT: Kendrick Press. 203--231 (2010; Zbl 1310.62043) Full Text: Link