Average Run Lengths of an Optimal Method of Detecting a Change in Distribution.

By Moshe Pollak. 1987

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

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]).”
Optimal sequential detection in multi-stream data (2015, background): “[15] Pollak, M. (1985).”
Data-efficient minimax quickest change detection (2012, background): “rove that the above mentioned choice of thresholds meets the FAR constraint, we note that fRr n n rgis a martingale. Speciﬁcally, fR n ngis a martingale and the conditions of theorem 2.3 are satisﬁed [24]. Hence, E 1[R ˝ SR ˝ ] = 0: Since, E 1[R ˝ SR ] B, for B= 1 we have FAR(˝ SR ) = 1 E 1[R ˝ SR ]”
SEQUENTIAL ANALYSIS: SOME CLASSICAL PROBLEMS AND NEW CHALLENGES (2001, methodology): “…ratios is a martingale (even when the observations are dependent) plays a major role in the evaluation of operating characteristics of tests of hypotheses (c.f. Robbins and Siegmund (1970, 1973)); other martingales play similar roles in other contexts (e.g., Pollak (1987), Novikov (1990)).”
Efficient scalable schemes for monitoring a large number of data streams (2010, background): “Fifth, the log log γ term in (13) is not surprising, as it has also arisen in other contexts such as the changepoint problem with composite post-change distributions for one-parametric exponential families; see, for example, Theorem 4 of Pollak (1987), or § 3.2 of Lai (1995).”
Is Average Run Length to False Alarm Always an Informative Criterion? (2008, background): “In view of the history of sequential change-point detection problems for independent observations, which was studied by Shewhart (1931) and Page (1954) but not rigorously formulated and solved until between 1963 and 1990 (Shiryayev (1963), Lorden (1971), Moustakides (1986), Pollak (1985, 1987), Rito”
ON OPTIMALITY PROPERTIES OF THE SHIRYAEV-ROBERTS PROCEDURE (2007, unknown): “An approximation (cf. Pollak, 1987 ) E1NA A/ (2.12)”
Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures (2010, background): “It follows from Pollak [7] that for the SR procedure E∞TA = (A/ζ)(1 + o(1)), A→ ∞.”
On optimality of the Shiryaev-Roberts procedure for detecting a change in distribution (2009, methodology): “It can be also deduced from Pollak (1985, 1987) that the conventional SR procedure is asymptotically minimax for a low false alarm rate within an additive term of order O(1), i.e., it is only second-order asymptotically optimal.”
Asymptotic operating characteristics of an optimal change point detection in hidden Markov models (2004, background): “Roberts (1966) considered the non-Bayesian setting, and studied by simulation the average run length of this rule, and found it to be very good.”
Asymptotic Optimality of Change-Point Detection Schemes in General Continuous-Time Models (2006, background): “data models, asymptotic performance of various change-point detection procedures in a minimax context with the constraint on the mean time to false alarm is well understood (see, e.g., Basseville and Nikiforov, 1993; Beibel, 1996; Moustakides, 1986; Pollak, 1987; Ritov, 1990; Shiryaev, 1996; Siegmun”
Numerical Comparison of CUSUM and Shiryaev–Roberts Procedures for Detecting Changes in Distributions (2009, methodology): “ Also, for small values of θSiegmund’s corrected Brownian motion approximations are fairly accurate (cf. Siegmund, 1985). For the ShiryaevRoberts procedure, we used the following approximation due to Pollak (1987): ARL(TSR A ) ≈ A/v, 14 which is very accurate even for relatively small threshold valu”
Nonanticipating estimation applied to sequential analysis and changepoint detection (2005, background): “Moreover, it is typically true that [5]”