Asymptotically Optimal Methods for Sequential Change-Point Detection

• Main Author: Mei, Yajun
• Format: Others
• Language: en
• Published: 2003
• Online Access: https://thesis.library.caltech.edu/2231/1/mei_thesis.pdf; Mei, Yajun (2003) Asymptotically Optimal Methods for Sequential Change-Point Detection. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PY76-DM19. https://resolver.caltech.edu/CaltechETD:etd-05292003-133431 <https://resolver.caltech.edu/CaltechETD:etd-05292003-133431>

<p>This thesis studies sequential change-point detection problems in different contexts. Our main results are as follows:</p> <p>- 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.</p> <p>- 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.</p> <p>- 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.</p> <p>- 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.</p> <p>- 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.</p>