A large deviation theorem for weighted sums |
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Authors: | Stephen A. Book |
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Affiliation: | (1) Department of Mathematics, California State College, 90747 Dominguez Hills, Calif., USA |
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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(Sn>cn)–log , where Sn is the partial sum of a sequence of independent, identically distributed random variables X1, X2, ... and is a constant depending on X1. 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.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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