Self-Normalized Weak Invariance Principle for Mixing Sequences
In this article we give a necessary and su±cient condition for a selfnormalized weak invariance principle, in the case of a strictly stationary Á-mixing sequence fXjgj¸1. This is obtained under the assumptions that the function L(x) = EX2 1 1fjX1·xg is slowly varying at 1 and the mixing coe±cients satisfy Á1=2(n)
|Date of creation:||30 Mar 2005|
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- Shao, Q. M., 1995. "Strong Approximation Theorems for Independent Random Variables and Their Applications," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 107-130, January.
- Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
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