### Abstract

Let Xj, …,Xn be a sequence of non-degenerate, symmetric, independent identically distributed random variables, and let Sn(rn) denote their sum when the rn largest in modulus have been removed. We obtain necessary and sufficient conditions for asymptotic normality of the studentized version of Sn(rn), and compare this to the condition for asymptotic normality of the scalar normalized version. In particular, when rn = r these conditions are the same, but when rn → ∞ the former holds more generally.

Original language | English (US) |
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Pages (from-to) | 597-610 |

Number of pages | 14 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 109 |

Issue number | 3 |

DOIs | |

State | Published - 1991 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Griffin, P. S., & Mason, D. M. (1991). On the asymptotic normality of self-normalized sums.

*Mathematical Proceedings of the Cambridge Philosophical Society*,*109*(3), 597-610. https://doi.org/10.1017/S0305004100070018