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--- seminars:datasci:200220 [2020/02/13 19:33] – qyu
+++ seminars:datasci:200220 [2020/02/19 15:53] (current) – qyu
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+<WRAP centeralign>##Statistics  Seminar##\\ Hosted by Department of Mathematical Sciences</WRAP>
+  * Date: Thursday, February 20, 2020
+  * Time: 1:15pm -- 2:30pm
+  * Room: WH-100E
+  * Speaker: Kexuan Li (Binghamton University)
+  * Title: On the Minimax Performance of the Generalized Shiryaev-Roberts Quickest Change-Point Detection in Continuous Time
+<WRAP center box 80%>
+<WRAP centeralign>**//Abstract//**</WRAP>
+The topic of interest in the minimax performance of the
+Generalized Shiryaev-Roberts (GSR) quickest change-point detection
+in continuous time, where the aim is to control online the drift of
+standard Brownian motion observed ``live''. The specific minimax
+criterion considered is that proposed by Pollak (1985) who
+suggested to look at the maximal expected detection lag conditional
+on no false alarm having yet been sounded, with the maximization
+performed over all possible change-point locations. While the
+question as to which detection procedure minimizes Pollak's delay
+metric is still an open one (whether in discrete or in continuous
+time), the GSR procedure is currently believed to be the most
+promising lead in the quest for minimax optimality. Hence the
+interest in the GSR procedure and its various extensions. The
+contribution of this work is two-fold. First we offer exact
+closed-form formulae for the performance characteristics of the GSR
+procedure. With the aid of the formulae we then obtain tantalizing
+numerical evidence that the procedure might be nearly minimax
+optimal in the limit, as the false alarm risk vanishes. Potential
+strategies to prove this analytically are also discussed. Second,
+we look at the randomized version of the GSR procedure that was
+proposed by Pollak (1985). The idea is to sample the initial value
+of the GSR statistic from its so-called quasi-stationary
+distribution (long-term behavior conditional on extended survival).
+This approach is known to be nearly Pollak minimax, in discrete as
+well as in continuous time. However, the important question as to
+the rate of convergence to the unknown optimal delay is still
+unanswered. We obtain new tight lower- and upper-bounds for the cdf
+as well as for the pdf of the quasi-stationary distribution, and
+then use the bounds to quantify the convergence rate. On the side
+we also find all of the fractional moments of the quasi-stationary
+distribution.
+</WRAP>