Mei, Yajun (2003) Asymptotically optimal methods for sequential change-point detection. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05292003-133431
This thesis studies sequential change-point detection problems in different contexts. Our main results are as follows:
- We present a new formulation of the problem of detecting a change of the parameter value in a one-parameter exponential family. Asymptotically optimal procedures are obtained.
- We propose a new and useful definition of ?asymptotically optimal to first-order? procedures in change-point problems when both the pre-change distribution and the post-change distribution involve unknown parameters. In a general setting, we define such procedures and prove that they are asymptotically optimal.
- We develop asymptotic theory for sequential hypothesis testing and change-point problems in decentralized decision systems and prove the asymptotic optimality of our proposed procedures under certain conditions.
- We show that a published proof that the so-called modified Shiryayev-Roberts procedure is exactly optimal is incorrect. We also clarify the issues involved by both mathematical arguments and a simulation study. The correctness of the theorem remains in doubt.
- We construct a simple counterexample to a conjecture of Pollak that states that certain procedures based on likelihood ratios are asymptotically optimal in change-point problems even for dependent observations.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Subject Keywords:||asymptotic optimality; change-point detection; decentralized decision; multi-sensor; sequential detection; sequential testing|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||28 May 2003|
|Author Email:||myajun (AT) caltech.edu|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||30 May 2003|
|Last Modified:||26 Dec 2012 02:48|
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