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 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 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.

Robust Weighted Least Squares Estimation of Regression Parameter in the Presence of Outliers and Heteroscedastic Errors

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Bello Abdulkadir Rasheed ◽  
Robiah Adnan ◽  
Seyed Ehsan Saffari ◽  
Kafi Dano Pati
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Robust Regression ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Model Parameters ◽  
Constant Variance ◽  
Regression Parameters ◽  
M Estimation

In a linear regression model, the ordinary least squares (OLS) method is considered the best method to estimate the regression parameters if the assumptions are met. However, if the data does not satisfy the underlying assumptions, the results will be misleading. The violation for the assumption of constant variance in the least squares regression is caused by the presence of outliers and heteroscedasticity in the data. This assumption of constant variance (homoscedasticity) is very important in linear regression in which the least squares estimators enjoy the property of minimum variance. Therefor e robust regression method is required to handle the problem of outlier in the data. However, this research will use the weighted least square techniques to estimate the parameter of regression coefficients when the assumption of error variance is violated in the data. Estimation of WLS is the same as carrying out the OLS in a transformed variables procedure. The WLS can easily be affected by outliers. To remedy this, We have suggested a strong technique for the estimation of regression parameters in the existence of heteroscedasticity and outliers. Here we apply the robust regression of M-estimation using iterative reweighted least squares (IRWLS) of Huber and Tukey Bisquare function and resistance regression estimator of least trimmed squares to estimating the model parameters of state-wide crime of united states in 1993. The outcomes from the study indicate the estimators obtained from the M-estimation techniques and the least trimmed method are more effective compared with those obtained from the OLS.

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 Comparison of M Estimation, S Estimation, with MM Estimation to Get the Best Estimation of Robust Regression in Criminal Cases in Indonesia

2022 ◽  
Vol 18 (2) ◽  
pp. 251-260
Author(s):  
Malecita Nur Atala Singgih ◽  
Achmad Fauzan
Keyword(s):  
Regression Analysis ◽  
Robust Regression ◽  
Estimation Method ◽  
Least Square Method ◽  
Influential Factors ◽  
Least Square ◽  
Method Of Moment ◽  
Best Estimate ◽  
M Estimation ◽  
Mm Estimation

Crime incidents that occurred in Indonesia in 2019 based on Survey Based Data on criminal data sourced from the National Socio-Economic Survey and Village Potential Data Collection produced by the Central Statistics Agency recorded 269,324 cases. The high crime rate is caused by several factors, including poverty and population density. Determination of the most influential factors in criminal acts in Indonesia can be done with Regression Analysis. One method of Regression Analysis that is very commonly used is the Least Square Method. However, Regression Analysis can be used if the assumption test is met. If outliers are found, then the assumption test is not completed. The outlier problem can be overcome by using a robust estimation method. This study aims to determine the best estimation method between Maximum Likelihood Type (M) estimation, Scale (S) estimation, and Method of Moment (MM) estimation on Robust Regression. The best estimate of Robust Regression is the smallest Residual Standard Error (RSE) value and the largest Adjusted R-square. The analysis of case studies of criminal acts in Indonesia in 2019 showed that the best estimate was the S estimate with an RSE value of 4226 and an Adjusted R-square of 0.98  

Modeling of Non-Monotonic Hysteresis Behavior in VO2-Coated Microactuators

2012 ◽  
Author(s):  
Jun Zhang ◽  
Emmanuelle Merced ◽  
Nelson Sepúlveda ◽  
Xiaobo Tan
Keyword(s):  
Phase Transition ◽  
Solid Phase ◽  
Weighting Function ◽  
Linear Operators ◽  
Least Square ◽  
Hysteretic Behavior ◽  
Model Parameters ◽  
Temperature Hysteresis ◽  
Silicon Cantilever ◽  
Preisach Operator

Vanadium dioxide (VO2) undergoes a thermally induced solid-to-solid phase transition. A VO2-coated silicon cantilever demonstrates large change in its bending curvature across its phase transition. Due to phase transition and thermal expansion effects, the curvature – temperature hysteresis in VO2 actuators comes with a non-monotonic hysteretic behavior, introducing new challenges in its modeling. Motivated by the underlying physics, in this paper we present a novel model that combines a monotonic Preisach hysteresis operator with a linear operator. A constrained least square scheme is proposed to estimate the model parameters. For comparison purposes, we also consider a Preisach operator with a signed weighting function, and a hybrid model consisting of a monotonic Preisach operator for the curvature within the transition and linear operators outside the transition. Experimental results confirm the effectiveness of the proposed model.

Parameter Identification Research Based on ARX Model

2012 ◽  
Vol 190-191 ◽  
pp. 292-296
Author(s):  
Huai Yuan Liu ◽  
Jian Hua He ◽  
Song Chen
Keyword(s):  
System Identification ◽  
Programming Model ◽  
System Modeling ◽  
Estimation Method ◽  
Information Criterion ◽  
Least Square ◽  
Model Parameters ◽  
Least Square Estimation ◽  
Model Order ◽  
Arx Model

Based on the principle of the system identification, combined Simulink with System Identification Toolbox from MATLAB, the least square estimation method is selected to establish a system of ARX model, and Akaike Information Criterion (AIC) was used in the identification of model order, compared with the original model to study the fitting accuracy, and the validity of the model is examined by residual analysis. This approach overcomes the disadvantages of the complexity and difficulty in traditional programming model. Compared to other program identification method, it has a short modeling time, and it is clear, reliable, intuitive visual, good scalability. Furthermore, the model parameters, result and system can be easily modified, assessed and verified. This method of system modeling and simulation can be used for reference to aerospace and other fields.

scholarly journals ANOMALY IDENTIFICATION FROM SUPER-LOW FREQUENCY ELECTROMAGNETIC DATA FOR THE COALBED METHANE DETECTION

2016 ◽  
Vol XLI-B8 ◽  
pp. 449-452
Author(s):  
S. S. Zhao ◽  
N. Wang ◽  
J. Hui ◽  
X. Ye ◽  
Q. Qin
Keyword(s):  
Coalbed Methane ◽  
Random Noise ◽  
Estimation Method ◽  
Low Frequency ◽  
Least Square ◽  
Electromagnetic Signal ◽  
Gaussian Component ◽  
Observation Data ◽  
Electromagnetic Data ◽  
Class B

Natural source Super Low Frequency(SLF) electromagnetic prospecting methods have become an increasingly promising way in the resource detection. The capacity estimation of the reservoirs is of great importance to evaluate their exploitation potency. In this paper, we built a signal-estimate model for SLF electromagnetic signal and processed the monitored data with adaptive filter. The non-normal distribution test showed that the distribution of the signal was obviously different from Gaussian probability distribution, and Class B instantaneous amplitude probability model can well describe the statistical properties of SLF electromagnetic data. The Class B model parameter estimation is very complicated because its kernel function is confluent hypergeometric function. The parameters of the model were estimated based on property spectral function using Least Square Gradient Method(LSGM). The simulation of this estimation method was carried out, and the results of simulation demonstrated that the LGSM estimation method can reflect important information of the Class B signal model, of which the Gaussian component was considered to be the systematic noise and random noise, and the Intermediate Event Component was considered to be the background ground and human activity noise. Then the observation data was processed using adaptive noise cancellation filter. With the noise components subtracted out adaptively, the remaining part is the signal of interest, i.e., the anomaly information. It was considered to be relevant to the reservoir position of the coalbed methane stratum.

scholarly journals Forecasting by Stochastic Models to Inflow of Karkheh Dam at Iran

2017 ◽  
Vol 3 (5) ◽  
pp. 340-350 ◽  
Author(s):  
Karim Hamidi Machekposhti ◽  
Hossein Sedghi ◽  
Abdolrasoul Telvari ◽  
Hossein Babazadeh
Keyword(s):  
Stochastic Models ◽  
Estimation Method ◽  
Information Criterion ◽  
Optimal Operation ◽  
Least Square ◽  
Management Tool ◽  
Model Parameters ◽  
Diagnostic Checking ◽  
The One ◽  
Hydrometric Station

Forecasting the inflow of rivers to reservoirs of dams has high importance and complexity. Design and optimal operation of the dams is essential. Mathematical and analytical methods use for understanding estimating and prediction of inflow to reservoirs in the future. Various methods including stochastic models can be used as a management tool to predict future values of these systems. In this study stochastic models (ARIMA) are applied to records of mean annual flow Karkheh river entrance to Karkheh dam in the west of Iran. For this purpose we collected annual flow during the period from 1958/1959 to 2005/2006 in Jelogir Majin hydrometric station. The available data consists of 48 years of mean Annual discharge. Three types of ARIMA (p, d, q) models (0, 1, 1), (1, 1, 1) and (4, 1, 1) suggested, and the selected model is the one which give minimum Akaike Information Criterion (AIC). The Maximum Likelihood (ML), Conditional Least Square (CLS) and Unconditional Least Square (ULS) methods are used to estimate the model parameters. It is found that the model which corresponds to the minimum AIC is the (4, 1, 1) model in CLS estimation method. Port Manteau Lack of fit test and Residual Autocorrelation Function (RACF) test are applied as diagnostic checking. Forecasting of annual inflow for the period from 2006 to 2015 are compared with observed inflow for the same period and since agreement is very good adequacy of the selected model is confirmed.

scholarly journals Response Surface Model with Comparison of OLS Estimation and MM Estimation

2021 ◽  
Vol 5 (2) ◽  
pp. 273-283
Author(s):  
Salsabila Basalamah ◽  
Edy Widodo
Keyword(s):  
Response Surface ◽  
Robust Regression ◽  
Estimation Method ◽  
Least Square ◽  
Surface Model ◽  
Method Of Moment ◽  
Optimal Point ◽  
Rsm Model ◽  
Mm Estimation

Response Surface Method (RSM) is a collection of statistical techniques in the form of experiments and regression, as well as mathematics that is useful for developing, improving, and optimizing processes. In general, the determination of models in RSM is estimated by linear regression with Ordinary Least Square (OLS) estimation. However, OLS estimation is very weak in the presence of data identified as outliers, so in determining the RSM model a strong and resistant estimation is needed namely robust regression. One estimation method in robust regression is the Method of Moment (MM) estimation. This study aims to compare the OLS estimation and MM estimation method to get the optimal point of response in this case study. Comparison of the best estimation models using the parameters MSE and R^2 adj. The results of MM estimation give better results to the optimal response results in this case study.

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