Bump detection in heterogeneous Gaussian regression

Enikeeva, Farida; Munk, Axel; Werner, Frank

doi:10.3150/16-bej899

Cited by 22 publications

(15 citation statements)

References 47 publications

(116 reference statements)

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“…smoothness constraints, expressed through F, we consider the alternative that f is an element of a very specific set of candidate functions. We refer to [10] and [9], where systems of scaled and translated rectangle functions (bumps) in a direct setting were considered.…”

Section: Connection To Existing Literaturementioning

confidence: 99%

Minimax detection of localized signals in statistical inverse problems

Pohlmann¹,

Werner²,

Munk³

2021

Preprint

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We investigate minimax testing for detecting local signals or linear combinations of such signals when only indirect data is available. Naturally, in the presence of noise, signals that are too small cannot be reliably detected. In a Gaussian white noise model, we discuss upper and lower bounds for the minimal size of the signal such that testing with small error probabilities is possible. In certain situations we are able to characterize the asymptotic minimax detection boundary. Our results are applied to inverse problems such as numerical differentiation, deconvolution and the inversion of the Radon transform.

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Section: Connection To Existing Literaturementioning

confidence: 99%

Minimax detection of localized signals in statistical inverse problems

Pohlmann¹,

Werner²,

Munk³

2021

Preprint

Self Cite

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“…Remark 2.2. Recently Enikeeva et al (2015) considered an extension of the classical sparse signal detection problem in which the measurements are heteroscedastic, and derived the asymptotic constants of the detection boundary. In principle, a model similar in spirit to the one presented in that work could also be considered here as well, by assuming that measurements on active components not only have elevated means, but also variance different to 1.…”

Section: Problem Setupmentioning

confidence: 99%

“…The ideas of Enikeeva et al (2015) can be used to modify our detection procedure (in particular the Sequential Thresholding Test -see Algorithm 2) to craft a procedure that can deal with measurements of different variances. However, the question of heteroscedasticity for dynamically evolving signals is too rich to be dealt with in the present work.…”

Section: Problem Setupmentioning

confidence: 99%

Are there needles in a moving haystack? Adaptive sensing for detection of dynamically evolving signals

Castro¹,

Tánczos²

2019

Bernoulli

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In this paper we investigate the problem of detecting dynamically evolving signals. We model the signal as an n dimensional vector that is either zero or has s non-zero components. At each time step t ∈ N the non-zero components change their location independently with probability p. The statistical problem is to decide whether the signal is a zero vector or in fact it has non-zero components. This decision is based on m noisy observations of individual signal components collected at times t = 1, . . . , m. We consider two different sensing paradigms, namely adaptive and non-adaptive sensing. For non-adaptive sensing the choice of components to measure has to be decided before the data collection process started, while for adaptive sensing one can adjust the sensing process based on observations collected earlier. We characterize the difficulty of this detection problem in both sensing paradigms in terms of the aforementioned parameters, with special interest to the speed of change of the active components. In addition we provide an adaptive sensing algorithm for this problem and contrast its performance to that of non-adaptive detection algorithms.

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“…There is a huge literature on testing changes of a mean in a sequence of random variables, see, e.g., Basseville and Nikiforov (1993), Csörgo and Horváth (1997), Brodsky and Darkhovsky (1993), Chen and Gupta (2000) for some basics on various methods and models. Previous research related to changed segment type models has been done by Levin and Kline (1985), Commenges et al (1986), Yao (1993), Gombay (1994), Ramanayake and Gupta (2003), , Enikeeva et al (2018), Račkauskas and Wendler (2020), to name a few. Of course, formally the changed segment type alternative may be viewed as a special case of multiple change points model.…”

Section: Introductionmentioning

confidence: 99%

Testing mean changes by maximal ratio statistics

2021

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We propose a new test statistic MR ,n for detecting a changed segment in the mean, at unknown dates, in a regularly varying sample. Our model supports several alternatives of shifts in the mean, including one change point, constant, epidemic and linear form of a change. Our aim is to detect a short length changed segment * , assuming * ∕n to be small as the sample size n is large. MR ,n is built by taking maximal ratios of weighted moving sums statistics of four sub-samples. An important feature of MR ,n is to be scale free. We obtain the limiting distribution of ratio statistics under the null hypothesis as well as their consistency under the alternative. These results are extended from i.i.d. samples under H 0 to some dependent samples. To supplement theoretical results, empirical illustrations are provided by generating samples from symmetrized Pareto and Log-Gamma distributions. KeywordsChange-point detection • Changed segment in the mean • Epidemic change • Hölder norm statistics • Regularly varying random variables • Scan statistics Mathematics Subject Classification (2000) 62G10 • 60F17

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Bump detection in heterogeneous Gaussian regression

Cited by 22 publications

References 47 publications

Minimax detection of localized signals in statistical inverse problems

Minimax detection of localized signals in statistical inverse problems

Are there needles in a moving haystack? Adaptive sensing for detection of dynamically evolving signals

Testing mean changes by maximal ratio statistics

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