Scan statistics for detecting a local change in variance for two-dimensional normal data

Zhao, Bo; Glaz, Joseph

doi:10.1080/03610926.2015.1104354

Cited by 6 publications

(2 citation statements)

References 23 publications

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“…, is a natural candidate; see Theorem 1 of [4] in time series context, and [23] and [49] in spatial context. In particular, H 0 should be rejected for a large SS T .…”

Section: Testing For Signal Presence In Random Fieldsmentioning

confidence: 99%

Frequency domain bootstrap methods for random fields

Yau

Chen

2021

Electron. J. Statist.

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This paper develops a frequency domain bootstrap method for random fields on Z 2 . Three frequency domain bootstrap schemes are proposed to bootstrap Fourier coefficients of observations. Then, inversetransformations are applied to obtain resamples in the spatial domain. As a main result, we establish the invariance principle of the bootstrap samples, from which it follows that the bootstrap samples preserve the correct second-order moment structure for a large class of random fields. The frequency domain bootstrap method is simple to apply and is demonstrated to be effective in various applications including constructing confidence intervals of correlograms for linear random fields, testing for signal presence using scan statistics, and testing for spatial isotropy in Gaussian random fields. Simulation studies are conducted to illustrate the finite sample performance of the proposed method and to compare with the existing spatial block bootstrap and subsampling methods.

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“…, is a natural candidate; see Theorem 1 of [4] in time series context, and [23] and [49] in spatial context. In particular, H 0 should be rejected for a large SS T .…”

Section: Testing For Signal Presence In Random Fieldsmentioning

confidence: 99%

Frequency domain bootstrap methods for random fields

Yau

Chen

2021

Electron. J. Statist.

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“…Scan statistic approaches has been largely studied since J. Naus first published on the problem in the 1960s (Naus, 1982;Glaz et al, 2001). See Chen and Glaz (2016) or Zhao and Glaz (2017) for recent developments on the topic.…”

Section: Introductionmentioning

confidence: 99%

Duality Between the Local Score of One Sequence and Constrained Hidden Markov Model

Mercier

2021

Methodol Comput Appl Probab

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We are interested here in a theoretical and practical approach for detecting atypical segments in a multi-state sequence. We prove in this article that the segmentation approach through an underlying constrained Hidden Markov Model (HMM) is equivalent to using the maximum scoring subsequence (also called local score), when the latter uses an appropriate rescaled scoring function. This equivalence allows results from both HMM or local score to be transposed into each other. We propose an adaptation of the standard forward-backward algorithm which provides exact estimates of posterior probabilities in a linear time. Additionally it can provide posterior probabilities on the segment length and starting/ending indexes. We explain how this equivalence allows one to manage ambiguous or uncertain sequence letters and to construct relevant scoring functions. We illustrate our approach by considering the TM-tendency scoring function.

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The Scan Statistic for Multidimensional Data and Social Media Applications

Sparks,

Paris

2024

Handbook of Scan Statistics

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Scan statistics for detecting a local change in variance for two-dimensional normal data

Cited by 6 publications

References 23 publications

Frequency domain bootstrap methods for random fields

Frequency domain bootstrap methods for random fields

Duality Between the Local Score of One Sequence and Constrained Hidden Markov Model

The Scan Statistic for Multidimensional Data and Social Media Applications

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