A change-point problem and inference for segment signals

We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: to each point of a design is attached a binary label that indicates whether that point belongs to an unknown segment and this label is contaminated with noise. The endpoints of the unknown segment are the change-points. We study the minimal size of the segment which allows statistical detection in different scenarios, including when the endpoints are separated from the boundary of the domain of the design, or when they are separated from one another. We compare this minimal size with the minimax rates of convergence for estimation of the segment under the same scenarios. The aim of this extensive study of a simple yet fundamental version of the change-point problem is two-fold: understanding the impact of the location and the separation of the change points on detection and estimation and bringing insights about the estimation and detection of convex bodies in higher dimensions.

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Dynamic Functional Connectivity Change-Point Detection With Random Matrix Theory Inference

Frontiers in Neuroscience ◽

10.3389/fnins.2021.565029 ◽

2021 ◽

Vol 15 ◽

Author(s):

Jaehee Kim ◽

Woorim Jeong ◽

Chun Kee Chung

Keyword(s):

Functional Connectivity ◽

Random Matrix Theory ◽

Random Matrix ◽

Change Point ◽

Matrix Theory ◽

Change Point Detection ◽

Change Points ◽

Point Problem ◽

Change Point Problem ◽

Point Detection

To study the dynamic nature of brain activity, functional magnetic resonance imaging (fMRI) data is useful including some temporal dependencies between the corresponding neural activity estimates. Recent studies have shown that the functional connectivity (FC) varies according to time and location which should be incorporated into the model. Modeling this dynamic FC (DFC) requires time-varying measures of spatial region of interest (ROI) sets. To know about the DFC, change-point detection in FC is of particular interest. In this paper, we propose a method of detecting a change-point based on the maximum of eigenvalues via random matrix theory (RMT). From covariance matrices for FC of all ROI's, the temporal change-point of FC is decided by an RMT approach. Simulation results show that our proposed method can detect meaningful FC change-points. We also illustrate the effectiveness of our FC detection approach by applying our method to epilepsy data where change-points detected are explained by the changes in memory capacity. Our study shows the possibility of RMT based approach in DFC change-point problem and in studying the complex dynamic pattern of functional brain interactions.

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Change Point Problem in Security Vulnerability Discovery Model

2019 International Conference on Software Security and Assurance (ICSSA) ◽

10.1109/icssa48308.2019.00010 ◽

2019 ◽

Author(s):

Ankur Shukla ◽

Basel Katt

Keyword(s):

Change Point ◽

Point Problem ◽

Security Vulnerability ◽

Change Point Problem ◽

Vulnerability Discovery

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Testing for long memory in the presence of a general trend

Journal of Applied Probability ◽

10.1017/s0021900200019215 ◽

2001 ◽

Vol 38 (04) ◽

pp. 1033-1054 ◽

Cited By ~ 19

Author(s):

Liudas Giraitis ◽

Piotr Kokoszka ◽

Remigijus Leipus

Keyword(s):

Long Memory ◽

Change Point ◽

General Trend ◽

Quantitative Description ◽

Stationary Sequence ◽

Change Points ◽

Asymptotic Size ◽

Short Memory ◽

The Impact ◽

Do So

The paper studies the impact of a broadly understood trend, which includes a change point in mean and monotonic trends studied by Bhattacharyaet al.(1983), on the asymptotic behaviour of a class of tests designed to detect long memory in a stationary sequence. Our results pertain to a family of tests which are similar to Lo's (1991) modifiedR/Stest. We show that both long memory and nonstationarity (presence of trend or change points) can lead to rejection of the null hypothesis of short memory, so that further testing is needed to discriminate between long memory and some forms of nonstationarity. We provide quantitative description of trends which do or do not fool theR/S-type long memory tests. We show, in particular, that a shift in mean of a magnitude larger thanN-½, whereNis the sample size, affects the asymptotic size of the tests, whereas smaller shifts do not do so.

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Testing and estimating in the change-point problem of the spectral function

Lithuanian Mathematical Journal ◽

10.1007/bf00970969 ◽

1992 ◽

Vol 32 (1) ◽

pp. 15-29 ◽

Cited By ~ 13

Author(s):

L. Giraitis ◽

R. Leipus

Keyword(s):

Spectral Function ◽

Change Point ◽

Point Problem ◽

Change Point Problem

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On high-dimensional change point problem

Science China Mathematics ◽

10.1007/s11425-016-0058-5 ◽

2016 ◽

Vol 59 (12) ◽

pp. 2355-2378

Author(s):

BaiSuo Jin ◽

GuangMing Pan ◽

Qing Yang ◽

Wang Zhou

Keyword(s):

Change Point ◽

Dimensional Change ◽

High Dimensional ◽

Point Problem ◽

Change Point Problem

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Change-point problem with biostatistical applications

Wiley StatsRef: Statistics Reference Online ◽

10.1002/9781118445112.stat05493 ◽

2014 ◽

Author(s):

Yudi Pawitan

Keyword(s):

Change Point ◽

Point Problem ◽

Change Point Problem

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BAYESIAN IDENTIFICATION OF OUTLIERS AND CHANGE-POINTS IN MEASUREMENT ERROR MODELS

Advances in Complex Systems ◽

10.1142/s0219525905000567 ◽

2005 ◽

Vol 08 (04) ◽

pp. 433-449 ◽

Cited By ~ 8

Author(s):

FERNANDO A. QUINTANA ◽

PILAR L. IGLESIAS ◽

HELENO BOLFARINE

Keyword(s):

Linear Regression ◽

Outlier Detection ◽

Change Point ◽

Regression Models ◽

Point Problem ◽

Linear Regression Models ◽

Outlier Identification ◽

Change Point Problem ◽

Error In Variables ◽

The Relationship

The problem of outlier and change-point identification has received considerable attention in traditional linear regression models from both, classical and Bayesian standpoints. In contrast, for the case of regression models with measurement errors, also known as error-in-variables models, the corresponding literature is scarce and largely focused on classical solutions for the normal case. The main object of this paper is to propose clustering algorithms for outlier detection and change-point identification in scale mixture of error-in-variables models. We propose an approach based on product partition models (PPMs) which allows one to study clustering for the models under consideration. This includes the change-point problem and outlier detection as special cases. The outlier identification problem is approached by adapting the algorithms developed by Quintana and Iglesias [32] for simple linear regression models. A special algorithm is developed for the change-point problem which can be applied in a more general setup. The methods are illustrated with two applications: (i) outlier identification in a problem involving the relationship between two methods for measuring serum kanamycin in blood samples from babies, and (ii) change-point identification in the relationship between the monthly dollar volume of sales on the Boston Stock Exchange and the combined monthly dollar volumes for the New York and American Stock Exchanges.

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Nonparametric Change Point Diagnosis Method of Concrete Dam Crack Behavior Abnormality

Mathematical Problems in Engineering ◽

10.1155/2013/969021 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

Zhanchao Li ◽

Chongshi Gu ◽

Zhongru Wu

Keyword(s):

Statistical Model ◽

Change Point ◽

Hot Spot ◽

Test Method ◽

Point Problem ◽

Concrete Dam ◽

Change Point Problem ◽

Crack Behavior ◽

Diagnosis Method ◽

Nonparametric Statistical

The study on diagnosis method of concrete crack behavior abnormality has always been a hot spot and difficulty in the safety monitoring field of hydraulic structure. Based on the performance of concrete dam crack behavior abnormality in parametric statistical model and nonparametric statistical model, the internal relation between concrete dam crack behavior abnormality and statistical change point theory is deeply analyzed from the model structure instability of parametric statistical model and change of sequence distribution law of nonparametric statistical model. On this basis, through the reduction of change point problem, the establishment of basic nonparametric change point model, and asymptotic analysis on test method of basic change point problem, the nonparametric change point diagnosis method of concrete dam crack behavior abnormality is created in consideration of the situation that in practice concrete dam crack behavior may have more abnormality points. And the nonparametric change point diagnosis method of concrete dam crack behavior abnormality is used in the actual project, demonstrating the effectiveness and scientific reasonableness of the method established. Meanwhile, the nonparametric change point diagnosis method of concrete dam crack behavior abnormality has a complete theoretical basis and strong practicality with a broad application prospect in actual project.

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