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Dependent Samples

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Book cover Nonparametric Curve Estimation from Time Series

Part of the book series: Lecture Notes in Statistics ((LNS,volume 60))

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Abstract

Let (Zi)N be a sequence of random variables taking values in a metric vector space (either ℝd or a Banach space B) and Fn m (for n and m ∈ Z U {-∞, +∞}) be the σ-algebra generated by {Zi, n≤i≤m}. In this chapter we summarize some dependence structures and some basic results which are used in the sequel. If we say that (Zi)N is stationary, then it means strict stationarity. For the definition of ergodicity we refer to Ibragimov and Linnik (1971).

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Authors and Affiliations

  1. Hungarian Academy of Sciences, Technical University Budapest, Stoczek u. 2., 1521, Budapest, Hungary

    Lázió Györfi

  2. Rechts- und Staatswissenschaftliche Fakultät, Wirtschaftstheoretische Abteilung 11, Universität Bonn, Adenauerallee 24-26, 5300, Bonn, Germany

    Wolfgang Härdle

  3. Laboratoire de Statistique et Probabilités Unité associée C.N.R.S. 745, Université Paul Sabatier, 118, Route de Narbonne, 31062, Toulouse Cédex, France

    Pascal Sarda & Philippe Vieu

Authors
  1. Lázió Györfi
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  2. Wolfgang Härdle
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  3. Pascal Sarda
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  4. Philippe Vieu
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Editor information

Editors and Affiliations

  1. Hungarian Academy of Sciences, Technical University Budapest, Stoczek u. 2., 1521, Budapest, Hungary

    Lázió Györfi

  2. Rechts- und Staatswissenschaftliche Fakultät, Wirtschaftstheoretische Abteilung 11, Universität Bonn, Adenauerallee 24-26, 5300, Bonn, Germany

    Wolfgang Härdle

  3. Laboratoire de Statistique et Probabilités Unité associée C.N.R.S. 745, Université Paul Sabatier, 118, Route de Narbonne, 31062, Toulouse Cédex, France

    Pascal Sarda  & Philippe Vieu  & 

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© 1989 Springer-Verlag Berlin Heidelberg

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Györfi, L., Härdle, W., Sarda, P., Vieu, P. (1989). Dependent Samples. In: Györfi, L., Härdle, W., Sarda, P., Vieu, P. (eds) Nonparametric Curve Estimation from Time Series. Lecture Notes in Statistics, vol 60. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3686-3_2

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  • DOI: https://doi.org/10.1007/978-1-4612-3686-3_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97174-2

  • Online ISBN: 978-1-4612-3686-3

  • eBook Packages: Springer Book Archive

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