1. OPTIMAL GAUSSIAN APPROXIMATION FOR MULTIPLE TIME SERIES.
- Author
-
Karmakar, Sayar and Wei Biao Wu
- Subjects
TIME series analysis ,STOCHASTIC processes ,CENTRAL limit theorem ,SAMPLE size (Statistics) ,GAUSSIAN channels - Abstract
We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay rate of the functional dependence measure, we quantify the error bound of the Gaussian approximation using the sample size n and the moment condition. Under the assumption of pth finite moment, with p > 2, this can range from a worst case rate of n
1/2 to the best case rate of n1/p . [ABSTRACT FROM AUTHOR]- Published
- 2020
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