Optimal Detection of a Change in Distribution

By Moshe Pollak. 1985

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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]).”
MULTIVARIATE CUMULATIVE SUM CONTROL CHARTS BASED ON PROJECTION PURSUIT (2001, background): “The definitions of such optimality can be found, for example, in Pollak (1985) and Moustakides (1986).”
Asymptotic operating characteristics of an optimal change point detection in hidden Markov models (2004, methodology): “It is worth asking that while the SRP rule (2.5)–(2.7) is asymptotically minimax in the i.i.d. cases [Pollak (1985)], is it nontrivial whether this is still true for hidden Markov models?”
Optimal stopping times for detecting changes in distributions (1986, methodology): “In [5], following again a non-Bayesian approach, the criterion D(N) = supmEm{( N - m)/N ? m} is used.”
Efficient scalable schemes for monitoring a large number of data streams (2010, methodology): “…echnology on June 24, 2010 http://biom et.oxfordjournals.org D ow nloaded from Third, the idea of using the sum of some suitable statistics to construct detection schemes has been well documented in the literature, especially the celebrated Shiryaev–Roberts procedure; see also Pollak (1985, 2006).”
A novel approach to detection of intrusions in computer networks via adaptive sequential and batch-sequential change-point detection methods (2006, methodology): “For instance, in [18], a CUSUM procedure based on ranks has been proposed, and in [12], a Shiryaev–Roberts–Pollak procedure based on the sequential vectors of signs and ranks has been studied for the i.i.d. observations.”
ON OPTIMALITY PROPERTIES OF THE SHIRYAEV-ROBERTS PROCEDURE (2007, background): “By Theorem 1 of Pollak (1985), there exist a constant 0 < c∗ < ∞ and a sequence {ρi, ci}i=1 with ρi −−−→ i→∞ 0, ci −−−→ i→∞ c∗, such that NAB is the limit of the Bayes rules Tρi,ci as i → ∞.”
Data-efficient minimax quickest change detection (2012, background): “To detect a change in mean of a sequence of Gaussian observations in an i.i.d. setting, i.e., when f0 ∼ N (0, 1) and f1 ∼ N (µ, 1), µ 6= 0, the GLR rule discussed above (75) (with mα = n and m ′ α = 1) reduces to τv = inf { n ≥ 1 : max 0≤k n [ n∑ i=k |Sn − Sn|√ (n− k) ] ≥ b } .”
A review and discussion of prospective statistical surveillance in public health (2003, background): “Further reading on general statistical surveillance can be found in Shiryaev (1963, 1978), Pollak (1985), Moustakides (1986), Frisén and de Maré (1991), Frisén (1992, 2002), Srivastava andWu (1993), Siegmund andVenkatraman (1995), Lai (1995) andFrisén andWessman (1999).”
Sequential Change-Point Detection When the Pre- and Post-Change Parameters are Unknown (2010, methodology): “3) in Siegmund and Venkatraman (1995), which is related to an earlier rule proposed by Pollak and Siegmund (1991) under the assumption of known = 1 − 0 and having the form”
Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures (2010, methodology): “Pollak [6] tweaked the procedure by starting it off at a random RA 0 whose distribution is the quasi-stationary distribution QA of the SR statistic Rn, defined by QA(x) = lim n→∞ P∞(Rn 6 x|TA > n), (1.”
Asymptotic Optimality of Change-Point Detection Schemes in General Continuous-Time Models (2006, methodology): “…as a nonrandom, unknown parameter, Page’s CUSUM test (Page, 1954) and the randomized version of the Shiryaev–Roberts detection procedure proposed by Pollak (1985) are optimal with respect to the minimax expected detection delay, subject to a constraint on the mean time to false alarm (see…”
EARLY DETECTION OF A CHANGE IN POISSON RATE AFTER ACCOUNTING FOR POPULATION SIZE EFFECTS (2011, background): “Then, it is clear that T ∗x=d ≥ N∗SR. Observe that Un − n is a martingale for the Shiryaev-Robert statistics Un’s under P∞; by the Optional Stopping Theorem, we have E∞(UN − N) = E∞(U0) for the stopping time N = N∗SR, see Pollak (1985).”
Numerical Comparison of CUSUM and Shiryaev–Roberts Procedures for Detecting Changes in Distributions (2009, methodology): “Following the same principle, Pollak (1985) suggested a similar constrained optimization problem with Lorden’s measure L T replaced by SADD T .”