Sequential change-point detection when unknown parameters are present in the pre-change distribution

By Yajun Mei. 2006

97 citations recorded by the source corpus.

In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution f_θ and tries to minimize the detection delay for every possible post-change distribution g_λ. In this paper, motivated by a number of practical examples, we first consider the reverse question by specifying a required detection delay at a given post-change distribution and trying to minimize the frequency of false alarms for every possible pre-change distribution f_θ. We present asymptotically optimal procedures for one-parameter exponential families. Next, we develop a general theory for change-point problems when both the pre-change distribution f_θ and the post-change distribution g_λ involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations.

Subfields: Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

The structure of optimal private tests for simple hypotheses (2018, background): “Change-point detection has a long history in statistics and information theory (e.g. [She31, Pag54, Pag55, Shi63, Lor71, Pol85, Mou86, Pol87, Lai95, Kul01, Mei06, VB14]).”
Differentially Private Change-Point Detection (2018, background): “Change-point detection is a canonical problem in statistics that has been studied for nearly a century; selected results include [She31, Pag54, Shi63, Rob66, Lor71, Pol85, Pol87, Mou86, Lai95, Lai01, Kul01, Mei06, Mei08, Mei10, Cha17].”
Mean shift testing in correlated data (2011, methodology): “For such purpose, we would suggest a sequential analysis approach along the lines of Mei (2006).”
Is Average Run Length to False Alarm Always an Informative Criterion? (2008, methodology): “Because this lemma is a special case of Theorem 2.3 of Mei (2006a), we state it here without proof.”
On Upper-Confidence Bound Policies for Switching Bandit Problems (2011, methodology): “Motivated by the problems cited above, and following a paradigm widely used in the change-point detection literature (see [12, 21] and references therein), we focus on non-stationary environments where the distributions of the rewards undergo abrupt changes.”
Optimal sequential detection in multi-stream data (2015, background): “6) and the classical lower bound formula of Lorden is best established via the inequality in Mei [11], Proposition 2.”