seminars:datasci:200220
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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> | ||