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

Convolution Estima 

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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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