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Convergence in Distribution

  • Chapter
Asymptotics for Associated Random Variables

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Abstract

This chapter addresses central limit theorems, invariance principles and then proceeds to the convergence of empirical processes. The pathway will be to start with versions based on stationary variables and drop this assumption introducing the necessary control on the covariance structure. The techniques will be based on approximations of independent variables relying on a few inequalities established in Chap. 2. Once we have proved the first results, we will find characterizations of convergence rates with respect to the usual supnorm metric between distribution functions. A few applications to statistical estimation problems will be addressed in the final section of this chapter, as done in the previous one.

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Authors and Affiliations

  1. Department of Mathematics, CMUC, University of Coimbra, Coimbra, Portugal

    Paulo Eduardo Oliveira

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  1. Paulo Eduardo Oliveira
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Oliveira, P.E. (2012). Convergence in Distribution. In: Asymptotics for Associated Random Variables. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25532-8_4

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