Fourier Methods for Sequential Change Point Analysis in Autoregressive Models

Hušková, Marie; Kirch, Claudia; Meintanis, Simos G.

doi:10.1007/978-3-7908-2604-3_50

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…Mei, 2010), univariate nonparametric change (e.g. Hušková et al, 2010;Hlávka et al, 2016;Desobry et al, 2005), Bayesian online change point detection (e.g. Fearnhead and Liu, 2007), to name but a few.…”

Section: Relevant Literaturementioning

confidence: 99%

A Note on Online Change Point Detection

Yu,

Padilla,

Wang

et al. 2020

Preprint

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Online change point detection is originated in sequential analysis, which has been thoroughly studied for more than half century. A variety of methods and optimality results have been established over the years. In this paper, we are concerned with the univariate online change point detection problem allowing for all model parameters to change. We establish a theoretical framework to allow for more refined minimax results. This includes a phase transition phenomenon and a study of the detection delay under three forms of Type-I error controls. We also examine a common belief on the conservativeness of different Type-I error control strategies and provide results for potentially multiple change points scenarios.

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Section: Relevant Literaturementioning

confidence: 99%

A Note on Online Change Point Detection

Yu,

Padilla,

Wang

et al. 2020

Preprint

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“…upper bounding the probability of η < η. There is a vast body of existing literature on this topic, including Moustakides (1986), Ritov (1990), Lorden (1971), Lai (1981), Lai (1995), Lai (1998), Lai (2001), Lai and Xing (2010), Chu et al (1996), Aue and Horváth (2004), Aue et al (2009c), Kirch (2008), Hušková and Kirch (2012), Mei (2010), Hušková et al (2010), Hlávka et al (2016), Desobry et al (2005), Fearnhead and Liu (2007), He et al (2018), Kirch and Weber (2018), Kurt et al (2018), Chen (2019b), Gösmann (2019), Gösmann et al (2019), Dette and Gösmann (2019), Keshavarz et al (2018), Chen et al (2020), Siegmund (2013), Tartakovsky et al (2014), Namoano et al (2019), Maillard (2019) and Yu et al (2020), among others.…”

Section: What We Will Not Cover In This Surveymentioning

confidence: 99%

A review on minimax rates in change point detection and localisation

2020

Preprint

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This paper reviews recent developments in fundamental limits and optimal algorithms for change point analysis. We focus on minimax optimal rates in change point detection and localisation, in both parametric and nonparametric models. We start with the univariate mean change point analysis problem and review the state-of-the-art results in the literature. We then move on to more complex data types and investigate general principles behind the optimal procedures that lead to minimax rate-optimal results.

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