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Finite-sample distributions of self-normalized sums

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  • Kim, Jeong-Ryeol
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    Abstract

    Logan et al. (1973) analyze the limit probability distribution of the statistic sn(p) = Σi=1 Xi/(Σi=1 | Χj |^p)^1/p as n → ∞, when Xi is in the domain of attraciton of a stable law with stabilility index α. By simulations, we provide quantiles of the usual critical levels of the finite-sample distributions of the Student?s t-statistic as α tξ(n) = Sn (p) [(n −1) / (n − Sn^2(p))]^1/2 with p = 2 . The response surface method is used to provide approximate quantiles of the finite-sample distributions of the Student's t-statistic. -- Logan u.a. (1973) untersuchen die Grenzwahrscheinlichkeitsverteilung der Statistik,sn(p) = Σi=1 Xi/(Σi=1 | Χj |^p)^1/p as n → ∞, für den Fall, dass Xi im Anziehungsbereich eines stabilen Gesetzes mit Stabilitätsindex von α liegt. Mit Hilfe einer Simulation werden Quantile der üblicherweise verwendeten kritischen Niveaus für Verteilungen endlicher Stichprobenumfänge der Studentischen t-Statistik, α tξ(n) = Sn (p) [(n −1) / (n − Sn^2(p))]^1/2 mit p = 2 ermittelt. Die Antwort-Oberfläche-Methode gibt die approximierten Quantile der Verteilungen endlicher Stichprobenumfänge der t-Statistik in einer übersichtlichen Form an.

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    Bibliographic Info

    Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2003,02.

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    Date of creation: 2003
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    Handle: RePEc:zbw:bubdp1:4197

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    Cited by:
    1. Kurz-Kim, Jeong-Ryeol & Loretan, Mico, 2014. "On the properties of the coefficient of determination in regression models with infinite variance variables," Journal of Econometrics, Elsevier, vol. 181(1), pages 15-24.

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