Abstract
This paper deals with rates of convergence in the CLT for certain types of dependency. The main idea is to combine a modification of a theorem of Stein, requiring a coupling construction, with a dynamic set-up provided by a Markov structure that suggests natural coupling variables. More specifically, given a stationary Markov chain
We apply the general method to the study of two problems. In the first, we consider the antivoter chain
The same approach may also be applied in situations where a Markov chain does not appear in the original statement of a problem but is constructed as an auxiliary device. This is illustrated by considering weighted U-statistics. In particular we are able to unify and generalize some results on normal convergence for degenerate weighted U-statistics and provide rates.
Citation
Yosef Rinott.
Vladimir Rotar.
"On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted
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