## Sums, trimmed sums, and extremes |

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### Contents

A More Robust Approach | 1 |

Weak Convergence of Trimmed Sums | 55 |

Invariance Principles and SelfNormalizations for Sums Trimmed | 81 |

Copyright | |

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### Common terms and phrases

approach assume asymptotic distribution asymptotic normality Brownian bridges censored sums centering central limit theorem constants converges in distribution Corollary CSORGO D. M. MASON defined denote distribution function domain of attraction domain of partial empirical distribution empirical distribution function empirical process estimates exists extreme values finite fixed given HAEUSLER Hahn Hence holds identically distributed implies inequality infinitely divisible infinitely divisible laws iterated logarithm Kuelbs Lemma lim sup liminf limit laws limiting distribution Maller Math modulus trimming nondecreasing nondegenerate obtain op(l order statistics partial attraction partial sums Poisson Prob probabilistic probability problem proof of Theorem prove quantile function quantile processes rate of convergence sample satisfying scale Section self-normalized sequence Shorack stable law stochastically compact strong law subsequence subsequential limits summands sums of independent sums of order symmetric theory unique vector Weiner WELLNER zero