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  

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.

scholarly journals KAJIAN METODE ORDINARY LEAST SQUARE DAN ROBUST ESTIMASI M PADA MODEL REGRESI LINIER SEDERHANA YANG MEMUAT OUTLIER

2020 ◽  
Vol 11 (1) ◽  
pp. 21
Author(s):  
Zahrotul Aflakhah ◽  
Jajang Jajang ◽  
Agustini Tripena Br. Sb.
Keyword(s):  
Full Article ◽  
Regression Model ◽  
Sample Size ◽  
Regression Models ◽  
Estimation Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Simple Linear Regression ◽  
Ordinary Least Square ◽  
M Estimation

This research discusses about the Ordinary Least Squares (OLS) method and robust M-estimation method; compare between the Tukey bisquare and Huber weighting from simple linier regression models that contain outliers. Data are generated through simulation with the percentages of outliers and sample sizes. Each data will be formed into a simple linier regression model, then the percentage of outliers, RSE and MAD values are calculated. The results show that RSE and MAD values produced by a simple linear regression model with the OLS method are influenced by the percentage of outliers. However, the regression model of robust M-estimation with sample size 30, 60, 90, 120, and 150 results an unstable RSE values with the change of the percentage of outlier and the MAD values that are not affected by the percentage of outliers and sample size. The robust M-estimation method with Tukey Bisquare weighting is as good as the Huber weighting. Full Article

scholarly journals The Parameter Estimation of Double Exponential Pulse Based on a Least Infinity Norm Fitting Method

2021 ◽  
Vol 2083 (4) ◽  
pp. 042002
Author(s):  
Yuewu Shi ◽  
Wei Wang ◽  
Zhizhen Zhu ◽  
Xin Nie
Keyword(s):  
Estimation Error ◽  
Estimation Method ◽  
Maximum Amplitude ◽  
Least Square Method ◽  
Least Square ◽  
Physical Parameters ◽  
Infinity Norm ◽  
Fitting Method ◽  
Double Exponential ◽  
Exponential Pulse

Abstract This paper presents an estimation method of double exponential pulse (DEP) between the physical parameters rise time (t r), full width at half maximum amplitude (t FWHM) and the mathematical parameters α, β. A newly fitting method based on the least infinity norm criterion is proposed to deal with the estimation problem of DEP. The calculation process and equation of parameters of this method is proposed based on an m-th-order polynomial fitting model. This estimation method is compared with the least square method by the same data and fitting function. The results show that the maximum estimation error of parameters of double exponential pulse obtained by the least infinity norm method is 1.5 %.

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 M ESTIMATION, S ESTIMATION, AND MM ESTIMATION IN ROBUST REGRESSION

2014 ◽  
Vol 91 (3) ◽  
Author(s):  
Y. Susanti ◽  
H. Pratiwi ◽  
S. Sulistijowati H. ◽  
T. Liana
Keyword(s):  
Robust Regression ◽  
M Estimation ◽  
Mm Estimation

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 PENGARUH KEMAMPUAN KEUANGAN DAERAH TERHADAP PERTUMBUHAN EKONOMI DI WILAYAH SUMATERA SELATAN PERIODE 2005-2014

MOTIVASI ◽  
2017 ◽  
Vol 2 (1) ◽  
pp. 207
Author(s):  
Juairiah Juairiah
Keyword(s):  
Economic Growth ◽  
Regression Analysis ◽  
Panel Data ◽  
Design Methodology ◽  
Least Square Method ◽  
Least Square ◽  
Financial Capacity ◽  
Effect Estimation ◽  
Analysis Models ◽  
Estimation Models

Purpose – The study aims to determine how the influence of financial capacity of region on economic growth in Southern Sumatran Region in period 2005 to 2014.Design/methodology - The analysis was performed by multiple regression analysis models by a Pooled Least Square method and the fixed effect estimation models. The data used is panel data of five provinces in Southern Sumatra.Findings – The analysis showed that the financial capacity in Southern Sumatra region is significantly affecting the economic growth.

scholarly journals THE EFFECT OF ECONOMIC STRENGTH, GOVERNMENT DEBT, LEVEL OF DEMOCRACY, PUBLIC TRUST, AND LEVEL OF HAPPINESS ON CORRUPTION PERCEPTION

2020 ◽  
Vol 5 (1) ◽  
pp. 98
Author(s):  
Dedy Susanto
Keyword(s):  
Robust Regression ◽  
Government Debt ◽  
Public Trust ◽  
Method Of Moment ◽  
The Public ◽  
Debt Level ◽  
Corruption Perception ◽  
Mm Estimation ◽  
The Relationship ◽  
Positive Effect

This study aims to analyze the effect of economic strength, government debt, level of democracy, public trust in government, and level of happiness on corruption perception. Data consisting of 113 countries are used to determine the causal relationship between variables that have been collected. Robust Regression statistical test with Method of Moment (MM) estimation is used to analyze the relationship between variables. The test results show that economic strength, level of democracy, public trust, and level of happiness have a significant positive effect on corruption perception, while government debt has no significant effect on corruption perception. It can be concluded that the higher the economic strength, the level of democracy, the public trust, and the level of happiness, the higher the corruption perception in the country. High corruption perception indicates the cleanliness of the country from corruption.

scholarly journals A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

2020 ◽  
Vol 8 (2) ◽  
pp. 610-630 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Emrah Altun EA ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Estimation Method ◽  
Least Square Method ◽  
Least Square ◽  
Likelihood Method ◽  
Survival Times ◽  
New Model ◽  
Von Mises ◽  
Bootstrapping Method

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

Sign in / Sign up

Export Citation Format

Share Document