Large deviations of the sample mean in general vector spaces

Bahadur, R. R. ; Zabell, S. L. (1979) Large deviations of the sample mean in general vector spaces Annals of Probability, 7 (4). pp. 587-621. ISSN 0091-1798

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Let X1, X2, ··· be a sequence of i.i.d. random vectors taking values in a space V, let X-n = (X1 + ··· + Xn)/n, and for J ⊂ V let an(J) = n-1log P(X-n∈ J). A powerful theory concerning the existence and value of limn→∞ an(J) has been developed by Lanford for the case when V is finite-dimensional and X1 is bounded. The present paper is both an exposition of Lanford's theory and an extension of it to the general case. A number of examples are considered; these include the cases when X1 is a Brownian motion or Brownian bridge on the real line, and the case when X-n is the empirical distribution function based on the first n values in an i.i.d. sequence of random variables (the Sanov problem).

Item Type:Article
Source:Copyright of this article belongs to Institute of Mathematical Statistics.
Keywords:Random Vectors; Large Deviations; Entropy; Sanov's Theorem; Exponential Family; Maximum Likelihood
ID Code:27042
Deposited On:08 Dec 2010 12:48
Last Modified:17 May 2016 10:20

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