Abstract
Asymptotic representations are derived for large deviation probabilities of weighted sums of independent, identically distributed random variables. The main theorem generalizes a 1952 theorem of Chernoff which asserts that n −1 log P(S n>cn)→−log ρ, where S n is the partial sum of a sequence of independent, identically distributed random variables X 1, X 2, ... and ρ is a constant depending on X 1. The main result is similar in form to, but different in focus from, a particular case of Feller's (1969) theorem on large deviations for triangular arrays.
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This paper is based on work done for the author's doctoral dissertation written under Prof. Donald R. Truax of the University of Oregon, Eugene.
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Book, S.A. A large deviation theorem for weighted sums. Z. Wahrscheinlichkeitstheorie verw Gebiete 26, 43–49 (1973). https://doi.org/10.1007/BF00533959
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DOI: https://doi.org/10.1007/BF00533959