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Three new concentration inequalities for time series data

Fang Han (University of Washington Statistics)
Monday, March 5, 2018 - 2:30pm to 3:20pm
LOW 101
Abstract: This talk contains two appetizers and one main dish. For the appetizers, I will introduce two exponential inequalities of U-statistics for weakly dependent data: one Hoeffding inequality for non-degenerate U-statistics, and one Bernstein inequality for degenerate ones, under different kernel assumptions and different weak dependence conditions, and using different proof techniques. For the main course, I will introduce a new concentration inequality for large autocovariance matrices constructed from high dimensional structural time series. It extends the inequality for product measures of Rudelson, and the proof method is based on the Cantor-set blocking argument put forward by Merlevede et al. (2011) and Banna et al. (2016) in case of geometrically strongly mixing scalar-valued or absolutely regular matrix-valued sequences. Applications include linear VAR(d) and vector-valued ARCH models.
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