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Moment Convergence in Conditional Limit Theorems
Journal of Applied Probability
Vol. 38, No. 2 (Jun., 2001), pp. 421-437
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3215897
Page Count: 17
You can always find the topics here!Topics: Perceptron convergence procedure, Integers, Cinerary urns, Mathematical theorems, Conditional convergence, Random variables, Mathematical moments, Hash coding, Statism, Integrands
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Consider a sum ∑2 N Yi of random variables conditioned on a given value of the sum ∑1 N Xi of some other variables, where Xi and Yi are dependent but the pairs (Xi, Yi) form an i.i.d. sequence. We consider here the case when each Xi is discrete. We prove, for a triangular array ((Xni, Yni)) of such pairs satisfying certain conditions, both convergence of the distribution of the conditioned sum (after suitable normalization) to a normal distribution, and convergence of its moments. The results are motivated by an application to hashing with linear probing; we give also some other applications to occupancy problems, random forests, and branching processes.
Journal of Applied Probability © 2001 Applied Probability Trust