SEQUENTIAL ANALYSIS: SOME CLASSICAL PROBLEMS AND NEW CHALLENGES

By Tze Leung Lai. 2001

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Citations in the corpus

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].”
Sequential Decision-Making under Non-stationary Environments via Sequential Change-point Detection (2014, methodology): “This research domain started with the seminal work of [16] that has been actively developed [10] ever since.”
Finite sample change point inference and identification for high‐dimensional mean vectors (2017, methodology): “Change point testing and estimation have a long history [45, 46, 41, 16, 31, 49, 10, 20, 33, 6, 23, 13, 37, 29, 27, 22, 24, 40, 3, 4, 7, 51, 30] and there are two major lines of change point tests in literature: sequential tests and fixed sample size tests [34].”
A Change-Point Model for a Shift in Variance (2005, background): “Phase II application of the change-point problem with at least some parameters prespecified is addressed implicitly in Siegmund and Venkatraman (1994), Pollak and Siegmund (1991), and the excellent review paper by Lai (2001).”
Item Response Theory—A Statistical Framework for Educational and Psychological Measurement (2021, unknown): “These problems are major topics of sequential analysis; see Lai (2001) for a comprehensive review.”
Asymptotic operating characteristics of an optimal change point detection in hidden Markov models (2004, methodology): “To prove Theorem 1, we can make use of Theorem 3.1 for the one-dimensional case in Fuh and Lai (2001) as in the case of i.i.d. ξn [see Theorem 1 of Zhang (1988)].”
Kernel Change-point Analysis (2008, background): “Promising experimental results in temporal segmentation of mental tasks from BCI data and pop song indexation are presented.”
Fixed-Width Output Analysis for Markov Chain Monte Carlo (2006, background): “Sequential statistical procedures have a long history (see Lai 2001 for an overview and commentary).”
A Linear Response Bandit Problem (2013, background): “…problems was introduced by Robbins (1952), and since then numerous variants thereof have been studied extensively in many different contexts; we refer to Berry and Fristedt (1985), Gittins (1989), Lai (2001) and the recent book by Cesa–Bianchi and Lugosi (2006), as well as references therein.”
EARLY DETECTION OF A CHANGE IN POISSON RATE AFTER ACCOUNTING FOR POPULATION SIZE EFFECTS (2011, background): “For recent reviews, we refer to Basseville and Nikiforov (1993), Lai (2001), Peskir and Shiryaev (2006), and Poor and Hadjiliadis (2008).”
Woodroofe's One-Armed Bandit Problem Revisited (2009, unknown): “Here the objective is to test two (or more) treatments and eventually allocate the one with greater efficacy to incoming patients; see Lai (2001) for further discussion and references therein.”
Martingales in Sequential Analysis and Time Series, 1945-1985 ∗ (2009, background): “…related to continuous-time martingale theory (see Sellke and Siegmund, 1983 and Section V.6 and Appendix 3 of Siegmund, 1985) this period also witnessed a unified treatment of Bayes tests of composite hypotheses via likelihood ratio martingales and optimal stopping (see Lai, 2001, pp. 306–308).”
Sequential Generalized Likelihood Ratios and Adaptive Treatment Allocation for Optimal Sequential Selection (2006, methodology): “Another direction in the sequential selection literature is under the rubric of the multiarmed bandit problem, which replaces the PCS constraint (1.1) by an optimal expected total reward criterion; see Lai (2001) for a brief review.”
The Changepoint Model for Statistical Process Control (2003, methodology): “If a shift is signaled, then the most recent epoch j at which Sj = 0 gives the maximum likelihood estimate of the last instant before the mean shift (Lai, 2001).”
Nonparametric control chart based on change-point model (2009, unknown): “This is addressed in Pollak and Siegmund (1991), Siegmund and Venkatraman (1995), Lai (1995), Gombay (2000) and an excellent review paper by Lai (2001) which presented a summary of the methods as well as a class of sequential detection rules.”