scholarly journals Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 399 ◽  
Author(s):  
Marco Riani ◽  
Anthony C. Atkinson ◽  
Aldo Corbellini ◽  
Domenico Perrotta
Keyword(s):  
Robust Regression ◽  
Robust Statistics ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Breakdown Point ◽  
Parameter Estimates ◽  
Normal Density ◽  
Density Power Divergence ◽  
Numerical Minimization ◽  
Power Divergence

Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter α , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power α . We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey’s biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of α leading to more efficient parameter estimates.

scholarly journals Overcoming the Existence of Extreme Outlier Data by Using Robust MM Method Based on The Objective Function of Tukey bisquare

2018 ◽  
Vol 1 (1) ◽  
pp. 022-032
Author(s):  
Science Nature
Keyword(s):  
High Efficiency ◽  
Robust Regression ◽  
Weighting Function ◽  
Estimation Method ◽  
Breakdown Point ◽  
Error Component ◽  
Least Square ◽  
Model Parameters ◽  
Observation Data ◽  
Extreme Outlier

A widely used estimation method in estimating regression model parameters is the ordinary least square (OLS) that minimizes the sum of the error squares. In addition to the ease of computing, OLS is a good unbiased estimator as long as the error component assumption ()  in the given model is met. However, in the application, it is often encountered violations of assumptions. One of the violation types is the violation of distributed error assumption which is caused by the existence of the outlier on observation data. Thus, a solid method is required to overcome the existence of outlier, that is Robust Regression. One of the Robust Regression methods commonly used is robust MM method. Robust MM method is a combination of breakdown point and high efficiency. Results obtained based on simulated data generated using SAS software 9.2, shows that the use of objective weighting function tukey bisquare is able to overcome the existence of extreme outlier. Furthermore, it is determined that the value of tuning constant c with Robust MM method is 4.685 and it is obtained95% of efficiency. Thus, the obtained breakdown point is 50%.    

scholarly journals Robust Estimation for Bivariate Poisson INGARCH Models

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 367
Author(s):  
Byungsoo Kim ◽  
Sangyeol Lee ◽  
Dongwon Kim
Keyword(s):  
Robust Estimation ◽  
New South ◽  
Estimation Method ◽  
Real Data ◽  
Regularity Conditions ◽  
Density Power Divergence ◽  
Asymptotically Normal ◽  
South Wales ◽  
Power Divergence ◽  
Conditional Maximum

In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we consider a robust estimation method for bivariate Poisson INGARCH models while using the minimum density power divergence estimator. We demonstrate the proposed estimator is consistent and asymptotically normal under certain regularity conditions. Monte Carlo simulations are conducted to evaluate the performance of the estimator in the presence of outliers. Finally, a real data analysis using monthly count series of crimes in New South Wales and an artificial data example are provided as an illustration.

scholarly journals Response Surface Regression with LTS and MM-Estimator to Overcome Outliers on Red Roselle Flowers

Jurnal Varian ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 91-98
Author(s):  
Trianingsih Eni Lestari ◽  
Rike Desy Tri Yuansa Yuansa
Keyword(s):  
Response Surface ◽  
Plant Height ◽  
Robust Regression ◽  
Estimation Method ◽  
Breakdown Point ◽  
Fertilizer Application ◽  
Least Square ◽  
Surface Response Method ◽  
Response Surface Regression ◽  
Response Method

The surface response method is similar to the regression analysis method which uses procedures or ways of estimating the response function regression model based on the Ordinary Least Square (OLS) method. Unfortunately, using the quadratic method has no drawbacks because it is easily sensitive to assumption deviations due to outlier cases. One of the solutions to the outlier problem is using robust regression. The method of parameters in the regression is very diverse, but the methods used in this study are the Least Trimmed Square (LTS) and MM-estimator methods because both methods have a high breakdown point of nearly 50%. The variables studied were the response variable consisting of red roselle plant height (Y1) and red roselle flower weight (Y2). While the independent variables were soil moisture factor (X1) and NPK fertilizer application factor (X2). The purpose of this study is to estimate the response surface regression parameters. using the LTS and MM-estimator methods on data that contains outliers. The resulting model in data analysis shows the same result that the best model is using the LTS estimation method. The modeling result of plant height obtained an R-Square value of 98,27% with an error is 1,243. Meanwhile, for the red rosella plant flower weight model, the R-Square value was 97,31% with an error is 0.6632.

scholarly journals Overcoming the Existence of Extreme Outlier Data by Using Robust MM Method Based on The Objective Function of Tukey bisquare

2018 ◽  
Vol 1 (1) ◽  
pp. 022-032
Author(s):  
Science Nature
Keyword(s):  
High Efficiency ◽  
Robust Regression ◽  
Weighting Function ◽  
Estimation Method ◽  
Breakdown Point ◽  
Error Component ◽  
Least Square ◽  
Model Parameters ◽  
Observation Data ◽  
Extreme Outlier

A widely used estimation method in estimating regression model parameters is the ordinary least square (OLS) that minimizes the sum of the error squares. In addition to the ease of computing, OLS is a good unbiased estimator as long as the error component assumption ()  in the given model is met. However, in the application, it is often encountered violations of assumptions. One of the violation types is the violation of distributed error assumption which is caused by the existence of the outlier on observation data. Thus, a solid method is required to overcome the existence of outlier, that is Robust Regression. One of the Robust Regression methods commonly used is robust MM method. Robust MM method is a combination of breakdown point and high efficiency. Results obtained based on simulated data generated using SAS software 9.2, shows that the use of objective weighting function tukey bisquare is able to overcome the existence of extreme outlier. Furthermore, it is determined that the value of tuning constant c with Robust MM method is 4.685 and it is obtained95% of efficiency. Thus, the obtained breakdown point is 50%.    

scholarly journals fsdaSAS: A Package for Robust Regression for Very Large Datasets Including the Batch Forward Search

Stats ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 327-347
Author(s):  
Francesca Torti ◽  
Aldo Corbellini ◽  
Anthony C. Atkinson
Keyword(s):  
Robust Regression ◽  
Multivariate Data ◽  
Likelihood Estimation ◽  
Breakdown Point ◽  
Large Datasets ◽  
Parameter Estimates ◽  
The European Union ◽  
Robust Estimators ◽  
Forward Search ◽  
Very Large Datasets

The forward search (FS) is a general method of robust data fitting that moves smoothly from very robust to maximum likelihood estimation. The regression procedures are included in the MATLAB toolbox FSDA. The work on a SAS version of the FS originates from the need for the analysis of large datasets expressed by law enforcement services operating in the European Union that use our SAS software for detecting data anomalies that may point to fraudulent customs returns. Specific to our SAS implementation, the fsdaSAS package, we describe the approximation used to provide fast analyses of large datasets using an FS which progresses through the inclusion of batches of observations, rather than progressing one observation at a time. We do, however, test for outliers one observation at a time. We demonstrate that our SAS implementation becomes appreciably faster than the MATLAB version as the sample size increases and is also able to analyse larger datasets. The series of fits provided by the FS leads to the adaptive data-dependent choice of maximally efficient robust estimates. This also allows the monitoring of residuals and parameter estimates for fits of differing robustness levels. We mention that our fsdaSAS also applies the idea of monitoring to several robust estimators for regression for a range of values of breakdown point or nominal efficiency, leading to adaptive values for these parameters. We have also provided a variety of plots linked through brushing. Further programmed analyses include the robust transformations of the response in regression. Our package also provides the SAS community with methods of monitoring robust estimators for multivariate data, including multivariate data transformations.

Estimation of the Shape Evolution and the Growth History of an Embedded Crack by Fatigue Loading

2011 ◽  
Author(s):  
Koji Gotoh ◽  
Keisuke Harada ◽  
Yosuke Anai
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Fatigue Cracks ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Fatigue Loading ◽  
Shape Evolution ◽  
Crack Growth Behaviour ◽  
Embedded Crack

Fatigue life estimation for planar cracks, e.g. part-through surface cracks or embedded cracks is very important because most of fatigue cracks found in welded built-up structures show planar crack morphologies. Fatigue crack growth behaviour of an embedded crack in welded joints is investigated in this study. The estimation procedure of crack shape evolution for an embedded crack is introduced and validation of the estimation procedure of fatigue crack growth based on the numerical simulation of fatigue crack growth with EDS concept for an embedded crack is performed. The validity of the proposed shape evolution estimation method and the fatigue crack growth simulation based on the fracture mechanics approach with EDS concept are confirmed.

Outlier Detection in Linear Regression

2011 ◽  
pp. 510-550 ◽  
Author(s):  
A. A. M. Nurunnabi ◽  
A. H. M. Rahmatullah Imon ◽  
A. B. M. Shawkat Ali ◽  
Mohammed Nasser
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Outlier Detection ◽  
Estimation Procedure ◽  
Support Vector ◽  
Parameter Estimates ◽  
Multivariate Statistical ◽  
Data Contamination ◽  
The People ◽  
Computational Simplicity

Regression analysis is one of the most important branches of multivariate statistical techniques. It is widely used in almost every field of research and application in multifactor data, which helps to investigate and to fit an unknown model for quantifying relations among observed variables. Nowadays, it has drawn a large attention to perform the tasks with neural networks, support vector machines, evolutionary algorithms, et cetera. Till today, least squares (LS) is the most popular parameter estimation technique to the practitioners, mainly because of its computational simplicity and underlying optimal properties. It is well-known by now that the method of least squares is a non-resistant fitting process; even a single outlier can spoil the whole estimation procedure. Data contamination by outlier is a practical problem which certainly cannot be avoided. It is very important to be able to detect these outliers. The authors are concerned about the effect outliers have on parameter estimates and on inferences about models and their suitability. In this chapter the authors have made a short discussion of the most well known and efficient outlier detection techniques with numerical demonstrations in linear regression. The chapter will help the people who are interested in exploring and investigating an effective mathematical model. The goal is to make the monograph self-contained maintaining its general accessibility.

Parameter Estimation in Marketing Models in the Presence of Influential Response Data: Robust Regression and Applications

1984 ◽  
Vol 21 (3) ◽  
pp. 268-277 ◽  
Author(s):  
Vijay Mahajan ◽  
Subhash Sharma ◽  
Yoram Wind
Keyword(s):  
Parameter Estimation ◽  
Regression Analysis ◽  
Least Squares ◽  
Robust Regression ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Parameter Estimates ◽  
Response Data ◽  
Marketing Models ◽  
Marketing Data

In marketing models, the presence of aberrant response values or outliers in data can distort the parameter estimates or regression coefficients obtained by means of ordinary least squares. The authors demonstrate the potential usefulness of the robust regression analysis in treating influential response values in marketing data.

Minimum density power divergence estimator for GARCH models

Test ◽  
2008 ◽  
Vol 18 (2) ◽  
pp. 316-341 ◽  
Author(s):  
Sangyeol Lee ◽  
Junmo Song
Keyword(s):  
Garch Models ◽  
Density Power Divergence ◽  
Minimum Density ◽  
Power Divergence
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