Bahadur, R. R. ; Zabell, S. L. (1979) Large deviations of the sample mean in general vector spaces Annals of Probability, 7 (4). pp. 587621. ISSN 00911798

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Official URL: http://www.projecteuclid.org/euclid.aop/1176994985
Related URL: http://dx.doi.org/10.1214/aop/1176994985
Abstract
Let X_{1}, X_{2}, ··· be a sequence of i.i.d. random vectors taking values in a space V, let X^{}_{n} = (X_{1} + ··· + X_{n})/n, and for J ⊂ V let a_{n}(J) = n^{1}log P(X^{}_{n}∈ J). A powerful theory concerning the existence and value of lim_{n→∞} a_{n}(J) has been developed by Lanford for the case when V is finitedimensional and X_{1} 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 X_{1} 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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