• Time: Thursday, May 2nd, 2019 at 5:30pm
  • Place: WEH 8220

A confidence sequence is a sequence of confidence intervals that is uniformly valid over an unbounded time horizon. In this paper, we develop confidence sequences whose widths go to zero, with non-asymptotic coverage guarantees under nonparametric conditions. Our technique draws a connection between the classical Cramér-Chernoff method for exponential concentration bounds, the law of the iterated logarithm (LIL), and the sequential probability ratio test—our confidence sequences extend the first to time-uniform concentration bounds; provide tight, non-asymptotic characterizations of the second; and generalize the third to nonparametric settings, including sub-Gaussian and Bernstein conditions, self-normalized processes, and matrix martingales. We illustrate the generality of our proof techniques by deriving an empirical-Bernstein bound growing at a LIL rate, as well as a novel upper LIL for the maximum eigenvalue of a sum of random matrices. Finally, we apply our methods to covariance matrix estimation and to estimation of sample average treatment effect under the Neyman-Rubin potential outcomes model.

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  • A preliminary talk will be given by Won Eui Hong at 4pm in WEH 7218 the same day.

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Food from Bangal Kebab will be served.