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Subsampling pp 213-252 | Cite as

Extrapolation, Interpolation, and Higher-Order Accuracy

  • Dimitris N. Politis
  • Joseph P. Romano
  • Michael Wolf
Part of the Springer Series in Statistics book series (SSS)

Abstract

In this chapter, we consider \( {{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{X}}_{n}} = ({X_{1}}, \ldots ,{X_{n}}) \) to be an observed stretch of a stationary, strong mixing sequence of real-valued random variables {Xt,t∈ℤ}. The probability measure generating the observations is again denoted by P. As mentioned in Appendix A, the strong mixing condition amounts to αx (k) = supA,B |P(AB) —P(A)P(B)|→0 as k tends to infinity, where A and B are events in the σ-algebras generated by {Xt,t < 0 } and {Xt, tk}, respectively. The case where X1,…, X n are independent, identically distributed (i.i.d.) will be treated here as an important special case where αx(k) = 0 for all k > 0.

Keywords

Mean Square Error Asymptotic Distribution Spectral Density Function Edgeworth Expansion Bootstrap Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Dimitris N. Politis
    • 1
  • Joseph P. Romano
    • 2
  • Michael Wolf
    • 3
  1. 1.Department of MathematicsUniversity of CaliforniaSan DiegoLa JollaUSA
  2. 2.Department of StatisticsStanford UniversityStanfordUSA
  3. 3.Departamento de Estadistica y EconometriaUniversidad Carlos III de MadridGetafeSpain

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