Finite-sample distributions of self-normalised sums

Jeong-Ryeol Kim ()

Computational Statistics, 2003, vol. 18, issue 3, 493-504

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

Keywords: Domain of attraction; α-table distributions; Student’s t-statistic; Finite-sample distributions; Response surface regression (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/BF03354612

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