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April 2002 Weak dependence beyond mixing and asymptotics for nonparametric regression
Peter Bühlmann, Paul Doukhan, Patrick Ango Nze
Ann. Statist. 30(2): 397-430 (April 2002). DOI: 10.1214/aos/1021379859


We consider a new concept of weak dependence, introduced by Doukhan and Louhichi [Stochastic Process. Appl. 84 (1999) 313–342], which is more general than the classical frameworks of mixing or associated sequences. The new notion is broad enough to include many interesting examples such as very general Bernoulli shifts, Markovian models or time series bootstrap processes with discrete innovations.

Under such a weak dependence assumption, we investigate nonparametric regression which represents one (among many) important statistical estimation problems. We justify in this more general setting the “whitening by windowing principle” for nonparametric regression, saying that asymptotic properties remain in first order the same as for independent samples. The proofs borrow previously used strategies, but precise arguments are developed under the new aspect of general weak dependence.


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Peter Bühlmann. Paul Doukhan. Patrick Ango Nze. "Weak dependence beyond mixing and asymptotics for nonparametric regression." Ann. Statist. 30 (2) 397 - 430, April 2002.


Published: April 2002
First available in Project Euclid: 14 May 2002

zbMATH: 1012.62037
MathSciNet: MR1902893
Digital Object Identifier: 10.1214/aos/1021379859

Primary: 60F05 , 62M99
Secondary: 60E15 , 60G10 , 60G99 , 62G07 , 62G09

Keywords: Bernoulli shift , bootstrap , central limit theorem , Lindeberg method , Markov process , Mixing , nonparametric estimation , Positive dependence , stationary sequence , time series

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 2 • April 2002
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