Functional CLT for nonparametric estimates of the spectrum and change-point problem for a spectral function

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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A change-point problem and inference for segment signals

ESAIM Probability and Statistics ◽

10.1051/ps/2018014 ◽

2018 ◽

Vol 22 ◽

pp. 210-235

Author(s):

Victor-Emmanuel Brunel

Keyword(s):

Change Point ◽

Rates Of Convergence ◽

Extensive Study ◽

Change Points ◽

Point Problem ◽

Minimal Size ◽

Detection And Estimation ◽

Change Point Problem ◽

Minimax Rates ◽

The Impact

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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Image analysis based on change point problem for random processes with the absence of a-priori data

10.1117/12.295628 ◽

1997 ◽

Author(s):

Salavat T. Kussimov ◽

Albert H. Sultanov ◽

Nail K. Bakirov ◽

Sergey V. Dyblenko

Keyword(s):

Image Analysis ◽

Change Point ◽

A Priori ◽

Random Processes ◽

Point Problem ◽

Change Point Problem

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Application of Change-Point Problem to the Detection of Plant Patches

Acta Biotheoretica ◽

10.1007/s10441-009-9093-x ◽

2009 ◽

Vol 58 (1) ◽

pp. 51-63 ◽

Cited By ~ 5

Author(s):

I. López ◽

M. Gámez ◽

J. Garay ◽

T. Standovár ◽

Z. Varga

Keyword(s):

Change Point ◽

Point Problem ◽

Change Point Problem

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Nonparametric point estimators for the change-point problem

Communication in Statistics- Theory and Methods ◽

10.1080/03610928808829826 ◽

1988 ◽

Vol 17 (11) ◽

pp. 3645-3675 ◽

Cited By ~ 4

Author(s):

Stephen M. scariano ◽

Terry A. watkins

Keyword(s):

Change Point ◽

Point Problem ◽

Change Point Problem ◽

Point Estimators

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