Robust change point detection for linear regression models

2019 ◽  
Vol 12 (2) ◽  
pp. 203-213
Author(s):  
Aylin Alin ◽  
Ufuk Beyaztas ◽  
Michael A. Martin
Keyword(s):  
Linear Regression ◽  
Change Point ◽  
Regression Models ◽  
Change Point Detection ◽  
Linear Regression Models ◽  
Point Detection

scholarly journals Online Change-Point Detection of Linear Regression Models

2019 ◽  
Vol 67 (12) ◽  
pp. 3316-3329
Author(s):  
Jun Geng ◽  
Bingwen Zhang ◽  
Lauren M. Huie ◽  
Lifeng Lai
Keyword(s):  
Linear Regression ◽  
Change Point ◽  
Regression Models ◽  
Change Point Detection ◽  
Linear Regression Models ◽  
Point Detection

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

2005 ◽  
Vol 08 (04) ◽  
pp. 433-449 ◽  
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.

INTERVAL PIECEWISE REGRESSION MODEL WITH AUTOMATIC CHANGE-POINT DETECTION BY QUADRATIC PROGRAMMING

2005 ◽  
Vol 13 (03) ◽  
pp. 347-361 ◽  
Author(s):  
JING-RUNG YU ◽  
GWO-HSHIUNG TZENG ◽  
HAN-LIN LI
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Regression Model ◽  
Change Point ◽  
Regression Models ◽  
Change Point Detection ◽  
Fuzzy Regression ◽  
Programming Approach ◽  
Piecewise Regression ◽  
Point Detection

To handle large variation data, an interval piecewise regression method with automatic change-point detection by quadratic programming is proposed as an alternative to Tanaka and Lee's method. Their unified quadratic programming approach can alleviate the phenomenon where some coefficients tend to become crisp in possibilistic regression by linear programming and also obtain the possibility and necessity models at one time. However, that method can not guarantee the existence of a necessity model if a proper regression model is not assumed especially with large variations in data. Using automatic change-point detection, the proposed method guarantees obtaining the necessity model with better measure of fitness by considering variability in data. Without piecewise terms in estimated model, the proposed method is the same as Tanaka and Lee's model. Therefore, the proposed method is an alternative method to handle data with the large variations, which not only reduces the number of crisp coefficients of the possibility model in linear programming, but also simultaneously obtains the fuzzy regression models, including possibility and necessity models with better fitness. Two examples are presented to demonstrate the proposed method.

Detection of a change-point in student-t linear regression models

2006 ◽  
Vol 47 (1) ◽  
pp. 31-48 ◽  
Author(s):  
Felipe Osorio ◽  
Manuel Galea
Keyword(s):  
Linear Regression ◽  
Change Point ◽  
Regression Models ◽  
Linear Regression Models

scholarly journals Comparison of Simple and Segmented Linear Regression Models on the Effect of Sea Depth toward the Sea Temperature

2021 ◽  
Vol 1 (2) ◽  
pp. 68-75
Author(s):  
Muhammad Bayu Nirwana ◽  
Dewi Wulandari
Keyword(s):  
Linear Regression ◽  
Linear Regression Model ◽  
Change Point ◽  
Regression Models ◽  
Linear Regression Models ◽  
Likelihood Estimator ◽  
Sea Temperature ◽  
Independent Variables ◽  
Modeling Data ◽  
The Relationship

The linear regression model is employed when it is identified a linear relationship between the dependent and independent variables. In some cases, the relationship between the two variables does not generate a linear line, that is, there is a change point at a certain point. Therefore, themaximum likelihood estimator for the linear regression does not produce an accurate model. The objective of this study is to presents the performance of simple linear and segmented linear regression models in which there are breakpoints in the data. The modeling is performed onthe data of depth and sea temperature. The model results display that the segmented linear regression is better in modeling data which contain changing points than the classical one.Received September 1, 2021Revised November 2, 2021Accepted November 11, 2021

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