scholarly journals Robust Geographically Weighted Regression Modeling using Least Absolute Deviation and M-Estimator

2019 ◽  
pp. 238-245
Author(s):  
Puteri Pekerti Wulandari ◽  
Anik Djuraidah ◽  
Aji Hamim Wigena
Keyword(s):  
Parameter Estimation ◽  
Geographically Weighted Regression ◽  
Location Parameter ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Regression ◽  
Absolute Deviation ◽  
Estimated Parameters ◽  
M Estimator ◽  
Better Than

Geographically weighted regression (GWR) is development of multiple regression that has spatial varying, so that the estimator of GWR is different for each location. Parameter estimation in GWR uses weighted least square method which is vulnerable to outlier and can cause biased parameter estimation. The robust GWR (RGWR) with LAD and M-estimator is resistance to outliers. This research estimated parameters on RGWR using LAD and M-estimator method and uses data of Java gross domestic product (GRDP) in 2015 containing several outliers. The result showed that RGWR model was better than GWR with M-estimator, and the predictions were closer to the actual values.

scholarly journals Parameter estimation of geographically weighted regression (GWR) model using weighted least square and its application

2018 ◽  
Author(s):  
Saskya Mary Soemartojo ◽  
Rima Dini Ghaisani ◽  
Titin Siswantining ◽  
Mariam Rahmania Shahab ◽  
Moch. Muchid Ariyanto
Keyword(s):  
Parameter Estimation ◽  
Geographically Weighted Regression ◽  
Least Square ◽  
Weighted Regression ◽  
Weighted Least Square ◽  
Gwr Model

scholarly journals ROBUST GEOGRAPHICALLY WEIGHTED REGRESSION DENGAN METODE MUTLAK SIMPANGAN TERKECIL PADA PEMODELAN KEJADIAN DIARE DI KOTA SEMARANG

2018 ◽  
Vol 7 (2) ◽  
pp. 143-152
Author(s):  
Ika Chandra Nurhayati ◽  
Agus Rusgiyono ◽  
Hasbi Yasin
Keyword(s):  
Spatial Heterogeneity ◽  
Spatial Data ◽  
Geographically Weighted Regression ◽  
Least Square ◽  
Weighted Regression ◽  
Distribution Data ◽  
Health Issues ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
The People

Diarrhea is one of many health issues in developing country like Indonesia, because the sickness and the death number are still high. According to health profile of Semarang City, the people who suffer from diarrhea from 2010-2015 are decreasing. The lowest point happened at the year 2013 with the total case of 38.001, however there are an increasing number from 2014-2015. The distribution data of diarrhea is a spatial data. The differences between environment and sanitation could cause spatial heterogeneity. The spatial heterogeneity could cause the produced variant value no longer constant, but instead it is different on each region. Therefore, regression model that involves the effects of spatial heterogeneity is needed, which are Geographically Weighted Regression (GWR) that is built by Weighted Least Square (WLS) adjuster. Although, GWR parameter adjuster that used WLS is very sensitive with the existence of outliers. The existence of the outlier in the data will create a huge residual. Thus, more robust method is needed, which is Least Absolute Deviation (LAD) methods in order to estimate the parameter on model GWR. This model is called Robust GWR (RGWR). The result shows that the model events of diarrhea on each region in Semarang City are different. Furthermore, the model events of diarrhea with RGWR model generate MAPE 16,3396% which means the performance of RGWR is formed well. Keyword: Diarrhea, Robust, Geographically Weighted Regression, Least Absolute Deviation

Second-hand housing batch evaluation model of zhengzhou city based on big data and MGWR model

2021 ◽  
pp. 1-20
Author(s):  
Chaojie Liu ◽  
Jie Lu ◽  
Wenjing Fu ◽  
Zhuoyi Zhou
Keyword(s):  
Real Estate ◽  
Geographically Weighted Regression ◽  
Euclidean Distance ◽  
Evaluation Model ◽  
Housing Prices ◽  
Information Criterion ◽  
Access Point ◽  
Least Square ◽  
Weighted Regression ◽  
Spatial Error

How to better evaluate the value of urban real estate is a major issue in the reform of real estate tax system. So the establishment of an accurate and efficient housing batch evaluation model is crucial in evaluating the value of housing. In this paper the second-hand housing transaction data of Zhengzhou City from 2010 to 2019 was used to model housing prices and explanatory variables by using models of Ordinary Least Square (OLS), Spatial Error Model (SEM), Geographically Weighted Regression (GWR), Geographically and Temporally Weighted Regression (GTWR), and Multiscale Geographically Weighted Regression (MGWR). And a correction method of Barrier Line and Access Point (BLAAP) was constructed, and compared with three correction methods previously studied: Buffer Area (BA), Euclidean Distance (ED), and Non-Euclidean Distance, Travel Distance (ND, TT). The results showed: The fitting degree of GWR, MGWR and GTWR by BLAAP was 0.03–0.07 higher than by ND. The fitting degree of MGWR was the highest (0.883) by BLAAP but the smallest by Akaike Information Criterion (AIC), and 88.3% of second-hand housing data could be well interpreted by the model.

scholarly journals Estimation of Error Variance-Covariance Parameters Using Multivariate Geographically Weighted Regression Model

2020 ◽  
Vol 2020 ◽  
pp. 1-5 ◽  
Author(s):  
Sri Harini
Keyword(s):  
Statistical Inference ◽  
Geographically Weighted Regression ◽  
Weighting Function ◽  
Likelihood Estimation ◽  
Error Variance ◽  
Least Square ◽  
Weighted Regression ◽  
Inference Procedure ◽  
Geographically Weighted Regression Model ◽  
Estimated Error

The Multivariate Geographically Weighted Regression (MGWR) model is a development of the Geographically Weighted Regression (GWR) model that takes into account spatial heterogeneity and autocorrelation error factors that are localized at each observation location. The MGWR model is assumed to be an error vector ε that distributed as a multivariate normally with zero vector mean and variance-covariance matrix Σ at each location ui,vi, which Σ is sized qxq for samples at the i-location. In this study, the estimated error variance-covariance parameters is obtained from the MGWR model using Maximum Likelihood Estimation (MLE) and Weighted Least Square (WLS) methods. The selection of the WLS method is based on the weighting function measured from the standard deviation of the distance vector between one observation location and another observation location. This test uses a statistical inference procedure by reducing the MGWR model equation so that the estimated error variance-covariance parameters meet the characteristics of unbiased. This study also provides researchers with an understanding of statistical inference procedures.

Minimum Zone Evaluation of Symmetry Error for Flatness to Flatness Based on the New Generation GPS

2013 ◽  
Vol 662 ◽  
pp. 887-891
Author(s):  
Qian Qian ◽  
Mei Fa Huang ◽  
Huan Yu Li
Keyword(s):  
Least Square Method ◽  
Mathematic Model ◽  
Least Square ◽  
Adaptive Genetic Algorithm ◽  
Machining Error ◽  
Minimum Zone ◽  
New Generation ◽  
Tolerance Method ◽  
The Mathematical Model ◽  
Better Than

Least square method (LSM) is the most popular method used to evaluate machining error nowadays. However, LSM is likely to overestimate the error value, therefore its solution is only approximate and rather than minimum. In order to obtain the minimum, we study the principle of the minimum zone tolerance method (MZT), analyze the characteristics of the new generation GPS, and give the minimum zone mathematic model of the symmetry error for flatness to flatness. For the purpose of optimizing the mathematical model, this paper describes the application of adaptive genetic algorithm to achieve the best estimation. Simultaneously, the process of optimization is realized by MALTAB. Finally, the experiment shows that the evaluation results of MZT is better than evaluation results of LSM.

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