Weak Dependence: With Examples and Applications (eBook)

Jérome Dedecker, Paul Doukhan, Gabriel Lang, José Rafael Leon, Sana Louhichi, Clémentine Prieur (Autoren)

eBook Download: PDF

2007 | 2007
XIV, 322 Seiten
Springer New York (Verlag)
978-0-387-69952-3 (ISBN)

Infos

This book develops Doukhan/Louhichi's 1999 idea to measure asymptotic independence of a random process. The authors, who helped develop this theory, propose examples of models fitting such conditions: stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Applications are still needed to develop a method of analysis for nonlinear times series, and this book provides a strong basis for additional studies.

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Time series and random ?elds are main topics in modern statistical techniques. They are essential for applications where randomness plays an important role. Indeed, physical constraints mean that serious modelling cannot be done - ing only independent sequences. This is a real problem because asymptotic properties are not always known in this case. Thepresentworkisdevotedtoprovidingaframeworkforthecommonlyused time series. In order to validate the main statistics, one needs rigorous limit theorems. In the ?eld of probability theory, asymptotic behavior of sums may or may not be analogous to those of independent sequences. We are involved with this ?rst case in this book. Very sharp results have been proved for mixing processes, a notion int- duced by Murray Rosenblatt [166]. Extensive discussions of this topic may be found in his Dependence in Probability and Statistics (a monograph published by Birkhau *ser in 1986) and in Doukhan (1994) [61], and the sharpest results may be found in Rio (2000)[161]. However, a counterexample of a really simple non-mixing process was exhibited by Andrews (1984) [2]. The notion of weak dependence discussed here takes real account of the available models, which are discussed extensively. Our idea is that robustness of the limit theorems with respect to the model should be taken into account. In real applications, nobody may assert, for example, the existence of a density for the inputs in a certain model, while such assumptions are always needed when dealing with mixing concepts.

Inhalt

Weak dependence.- Models.- Tools for non causal cases.- Tools for causal cases.- Applications of strong laws of large numbers.- Central Limit theorem.- Donsker Principles.- Law of the iterated logarithm (LIL).- The Empirical process.- Functional estimation.- Spectral estimation.- Econometric applications and resampling.

Produkt-Details

• Erscheint lt. Verlag: 29.7.2007
• Reihe/Serie: Lecture Notes in Statistics
• Reihe/Serie: Lecture Notes in Statistics
• Zusatzinfo: XIV, 322 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Fitting • parametric statistics • resampling • Statistics
• ISBN-10: 0-387-69952-X / 038769952X
• ISBN-13: 978-0-387-69952-3 / 9780387699523