Nonanticipating estimation applied to sequential analysis and changepoint detection
By G. Lorden, Moshe Pollak. 2005
65 citations recorded by the source corpus.
Suppose a process yields independent observations whose distributions belong to a family parameterized by theta E Theta. When the process is in control, the observations are i.i.d. with a known parameter value theta(0). When the process is out of control, the parameter changes. We apply an idea of Robbins and Siegmund [Proc. Sixth Berkeley Symp. Math. Statist. Probab. 4 (1972) 37-41] to construct a class of sequential tests and detection schemes whereby the unknown post-change parameters are estimated. This approach is especially useful in situations where the parametric space is intricate and mixture-type rules are operationally or conceptually difficult to formulate. We exemplify our approach by applying it to the problem of detecting a change in the shape parameter of a Gamma distribution, in both a univariate and a multivariate setting.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/59b0752ec2cd474ce49f09b81cac30f29f4a6c6b
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In Statistics and Probability
Citations in the corpus
- Uniform, nonparametric, non-asymptotic confidence sequences (2018, unknown): “This is similar to a generalized likelihood ratio but is modified to retain the martingale property (cf. Wald, 1947, §10.5, Lorden and Pollak, 2005).”
- Estimating means of bounded random variables by betting (2020, background): “(4)], Dawid [24], and Lorden and Pollak [52] as well as in the information theory literature [66].”