PROCEDURES FOR REACTING TO A CHANGE IN DISTRIBUTION

By G. Lorden. 1971

A problem of optimal stopping is formulated and simple rules are proposed which are asymptotically optimal in an appropriate sense. The problem is of central importance in quality control and also has applications in reliability theory and other areas.

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Citations in the corpus

Bayesian Online Changepoint Detection (2007, methodology): “Frequentist approaches to changepoint detection, from the pioneering work of Page [22, 23] and Lorden [19] to recent work using support vector machines [10], offer online changepoint detectors.”
Data-efficient minimax quickest change detection (2012, unknown): “Then the generalized CuSum (68) GLR and mixture based algorithms are given, respectively, by: τ̂G = inf { n ≥ 1 : max n−mα≤k≤n−m′α sup θ [ n∑ i=k log fθ,i(Xi|Xi−11 ) f0,i(Xi|Xi−11 ) ] ≥ cα } (75) and τ̂M = inf { n ≥ 1 : max n−mα≤k≤n [∫ n∏ i=k fθ,i(Xi|Xi−11 ) f0,i(Xi|Xi−11 ) dG(θ) ] ≥ ecα } .”
EARLY DETECTION OF A CHANGE IN POISSON RATE AFTER ACCOUNTING FOR POPULATION SIZE EFFECTS (2011, methodology): “Pioneering foundational work in the field includes Page (1954), Shiryaev (1963), Roberts (1966), Lorden (1971), Pollak (1985), Moustakides (1986), Ritov (1990), Yakir (1994), and Lai (1995).”
CUSUM and EWMA multi-charts for detecting a range of mean shifts (2007, methodology): “In fact, Lorden (1971) has already considered and studied such a model.”
Detecting relevant changes in time series models (2014, methodology): “On the one hand, we want to consider a CUSUM-type statistic, which has some optimality properties for testing the ‘classical’ change point hypothesis H0 : μ1 = μ2 (see for example Lorden (1971) and the subsequent literature for early references and Moustakides (2004) for a more recent reference).”
EWMA Control Charts for Monitoring Optimal Portfolio Weights (2007, background): “The alternative criteria of Roberts (1966), Lorden (1971), and Pollak and Siegmund (1975) are not considered here.”
A novel approach to detection of intrusions in computer networks via adaptive sequential and batch-sequential change-point detection methods (2006, methodology): “[8], [16], [24], [33] are useful for many applications but do not solve the problem when the distributions are not known.”
A Survey of Fault Detection, Isolation, and Reconfiguration Methods (2010, background): “The most significant early works in that direction are those by Shiryayev [110] and Lorden [111].”
A review of novelty detection (2014, methodology): “A related approach involves a class of methods which are part of the well-established field of changepoint detection [148,149].”
Efficient scalable schemes for monitoring a large number of data streams (2010, background): “It turns out (Lorden, 1971) that if Ē (k1,...,km )(T ) is finite, then P∞(T ∞) = 1, implying that we will have a false alarm sooner or later with probability 1 even when no event occurs.”
Martingales in Sequential Analysis and Time Series, 1945-1985 ∗ (2009, methodology): “random variables X1;X2;:::; such that P ( Lorden (1971) in relating the CUSUM rule to the one-sided SPRT.”
Numerical Comparison of CUSUM and Shiryaev–Roberts Procedures for Detecting Changes in Distributions (2009, methodology): “As we have mentioned in the Introduction, Lorden (1971) proposed to minimize the measure defined in (1.”
Finite sample change point inference and identification for high‐dimensional mean vectors (2017, background): “…hypothesis n = 0 and the out-control mean-shift hypothesis for a given n ≠ 0 in model (1), aiming to minimise the expected average run length (Chernoff & Zacks, 1964; Hinkley, 1970; Lai, 2001; Lorden, 1971; Page, 1955; Qiu, 2014; Wald, 1945; Wald & Wolfowitz, 1948; Woodall & Ncube, 1985).”