Gaussian Approximation for Nonlinear Multiple Time Series and Applications
Speaker:
Sayar Karmakar – assistant professor of statistics, University of Florida
Description:
We obtain an optimal bound for Gaussian approximation of a large class of vector-valued random processes. Our results substantially generalize earlier ones which assume independence and/or stationarity. Based on the decay rate of functional dependence measure, we quantify the error bound of the Gaussian approximation based on the sample size and the moment condition. Under the assumption of $p$-th finite moment, with $p>2$, this can range from the worst $n^{1/2}$ to the optimal $n^{1/p}$ rate. For the general audience, this talk also provides a brief tutorial on handling non-linear dependence through a functional dependence measure which is often more convenient than strong mixing conditions. We exhibit multiple applications of our Gaussian approximation in the regime of simultaneous inference for time-varying models and change-point analysis. We conclude the talk discussing some natural extension to spatial/tensor data under a general form of dependence.