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Asymptotic Statistics by A.W. van der Vaart

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2

Stochastic Convergence

           This chapter provides a review of basic modes of convergence of sequences of stochastic vectors, in particular convergence in distribution and in probability.

2.1 Basic Theory

A random vector in image is a vector X = (X1,..., Xk) of real random variables. The distribution function of X is the map x image P(Xx).

    A sequence of random vectors Xn is said to converge in distribution to a random vector X if

image

for every

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