## Abstract

We investigate some effects that the ‘light’ trimming of a sum S_{n} = X_{1} + X_{2} + . . . + X_{n} of independent and identically distributed random variables has on behaviour of iterated logarithm type. Light trimming is defined as removing a constant number of summands from S_{n}. We consider two versions: ^{(r)}S_{n}, which is obtained by deleting the r largest X_{i} from S_{n}, and ^{r}S_{n}, which is obtained by deleting the r variables X_{i} which are largest in absolute value from S_{n}. We summarise some relevant results from Rogozin (1968), Heyde (1969), and later writers concerning the untrimmed sum, and add some newresults concerning trimmed sums. Among other things we show that a general form of the law of the iterated logarithm holds for ^{(r)}S_{n} but not (completely) for ^{(r)}S_{n}.

Original language | English |
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Pages (from-to) | 253-271 |

Number of pages | 19 |

Journal | Journal of Applied Probability |

Volume | 41A |

DOIs | |

Publication status | Published - 2004 |

Externally published | Yes |