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Finite-sample distributions of self-normalised sums

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  • Jeong-Ryeol Kim

Abstract

(Logan, Mallows, Rice & Shepp 1973) analyse the limit probability distribution of the statistic ${S_n}\left( p \right)=\sum\nolimits_{i=1} {{X_i}/{{\left( {{{\sum\nolimits_{i=1} {|{X_j}|} }^p}} \right)}^{1/p}}}$ as n → ∞, when X{ini} is in the domain of attraction of a stable law with stability index α. By simulations, we provide quantiles of the usual critical levels of the finite-sample distributions of the Student\rss t-statistic as $_\alpha {t_\xi }\left( n \right)={S_n}\left( p \right){\left[ {\left( {n - 1} \right)/\left( {n - S_n^2\left( p \right)} \right)} \right]^{1/2}}$ with p=2. The response surface method is used to provide approximate quantiles of the finite-sample distributions of the Student’s t-statistic. Copyright Physica-Verlag 2003

Suggested Citation

  • Jeong-Ryeol Kim, 2003. "Finite-sample distributions of self-normalised sums," Computational Statistics, Springer, vol. 18(3), pages 493-504, September.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:3:p:493-504
    DOI: 10.1007/BF03354612
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    References listed on IDEAS

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    1. Weron, Rafal, 1996. "Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables"," MPRA Paper 20761, University Library of Munich, Germany, revised 2010.
    2. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
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