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The Bootstrap of the Mean for Dependent Heterogeneous Arrays

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  • Silvia Gonçalves
  • Halbert White

Abstract

Presently, conditions ensuring the validity of bootstrap methods for the sample mean of (possibly heterogeneous) near epoch dependent (NED) functions of mixing processes are unknown. A0501n purpose of this paper is thus to establish the validity of the bootstrap in this context, extending the applicability of bootstrap methods to a class of processes broadly relevant for applications in economics and finance. The results apply to the moving blocks bootstrap of Künsch (1989) and Liu and Singh (1992) as well as to the stationary bootstrap of Politis and Romano (1994). In particular, the consistency of the bootstrap variance estimator for the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first order asymptotic validity of the bootstrap approximation to the actual distribution of the sample mean is also established in this heterogeneous NED context. Actuellement, les conditions assurant la validité des méthodes de bootstrap pour la moyenne d'échantillon des (possiblement hétérogènes) fonctions de dépendance d'époque proche (DEP) des processus de mixage sont inconnues. Ainsi, un des objectifs principaux de cet article est d'établir la validité du bootstrap dans ce contexte, en élargissant l'applicabilité des méthodes de bootstrap à une classe de processus largement adéquats pour les applications en économie et en finance. Les résultats se rapportent au bootstrap de blocs mouvants de Künsch (1989) et Liu et Singh (1992), de même qu'au bootstrap stationnaire de Politis et Romano (1994). Plus particulièrement, nous démontrons que la consistance de l'estimateur de variance du bootstrap pour la moyenne d'échantillon résiste à l'hétéroscédasticité et à la dépendance de forme inconnue. La validité asymptotique de premier ordre de l'approximation du bootstrap à la distribution actuelle de la moyenne d'échantillon est également démontrée dans ce contexte DEP hétérogène.

Suggested Citation

  • Silvia Gonçalves & Halbert White, 2001. "The Bootstrap of the Mean for Dependent Heterogeneous Arrays," CIRANO Working Papers 2001s-19, CIRANO.
    • Handle: RePEc:cir:cirwor:2001s-19
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    References listed on IDEAS

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    More about this item

    Keywords

    Block bootstrap; near epoch dependence; sample mean; Bootstrap en bloc; dépendance d'époque proche; moyenne d'échantillon;
    All these keywords.

    JEL classification:

    • C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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