scholarly journals Analysis of Efficiency of Least Trimmed Square and Least Median Square Methods in The Estimation of Robust Regression Parameters

2020 ◽  
Vol 4 (1) ◽  
pp. 21
Author(s):  
Hamdan Abdi ◽  
Sajaratud Dur ◽  
Rina Widyasar ◽  
Ismail Husein
Keyword(s):  
Observational Data ◽  
Palm Oil ◽  
Regression Models ◽  
Robust Regression ◽  
Least Squares Method ◽  
Regression Method ◽  
Estimation Methods ◽  
Land Area ◽  
Regression Methods ◽  
Regression Parameters

<span lang="EN">Robust regression is a regression method used when the remainder's distribution is not reasonable, or there is an outreach to observational data that affects the model. One method for estimating regression parameters is the Least Squares Method (MKT). The method is easily affected by the presence of outliers. Therefore we need an alternative method that is robust to the presence of outliers, namely robust regression. Methods for estimating robust regression parameters include Least Trimmed Square (LTS) and Least Median Square (LMS). These methods are estimators with high breakdown points for outlier observational data and have more efficient algorithms than other estimation methods. This study aims to compare the regression models formed from the LTS and LMS methods, determine the efficiency of the model formed, and determine the factors that influence the production of community oil palm in Langkat District in 2018. The results showed that in testing, the estimated model of the regression parameters showed the same results. Compared to the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018</span>

scholarly journals PEMODELAN REGRESI RIDGE ROBUST-MM DALAM PENANGANAN MULTIKOLINIERITAS DAN PENCILAN (Studi Kasus : Faktor-Faktor yang Mempengaruhi AKB di Jawa Tengah Tahun 2017)

2019 ◽  
Vol 8 (1) ◽  
pp. 24-34
Author(s):  
Eka Destiyani ◽  
Rita Rahmawati ◽  
Suparti Suparti
Keyword(s):  
Least Squares ◽  
Robust Regression ◽  
Ordinary Least Squares ◽  
Regression Method ◽  
Predictor Variables ◽  
Healthy Life ◽  
Significance Level ◽  
Central Java ◽  
Regression Parameters

The Ordinary Least Squares (OLS) is one of the most commonly used method to estimate linear regression parameters. If multicollinearity is exist within predictor variables especially coupled with the outliers, then regression analysis with OLS is no longer used. One method that can be used to solve a multicollinearity and outliers problems is Ridge Robust-MM Regression. Ridge Robust-MM  Regression is a modification of the Ridge Regression method based on the MM-estimator of Robust Regression. The case study in this research is AKB in Central Java 2017 influenced by population dencity, the precentage of households behaving in a clean and healthy life, the number of low-weighted baby born, the number of babies who are given exclusive breastfeeding, the number of babies that receiving a neonatal visit once, and the number of babies who get health services. The result of estimation using OLS show that there is violation of multicollinearity and also the presence of outliers. Applied ridge robust-MM regression to case study proves ridge robust regression can improve parameter estimation. Based on t test at 5% significance level most of predictor variables have significant effect to variable AKB. The influence value of predictor variables to AKB is 47.68% and MSE value is 0.01538.Keywords:  Ordinary  Least  Squares  (OLS),  Multicollinearity,  Outliers,  RidgeRegression, Robust Regression, AKB.

TSS concentration in sewers estimated from turbidity measurements by means of linear regression accounting for uncertainties in both variables

2004 ◽  
Vol 50 (11) ◽  
pp. 81-88 ◽  
Author(s):  
J.-L. Bertrand-Krajewski
Keyword(s):  
Linear Regression ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Regression Method ◽  
Data Series ◽  
Time Interval ◽  
Sewer System ◽  
Regression Parameters ◽  
T Values ◽  
Ordinary Least Squares Method

In order to replace traditional sampling and analysis techniques, turbidimeters can be used to estimate TSS concentration in sewers, by means of sensor and site specific empirical equations established by linear regression of on-site turbidity T values with TSS concentrations C measured in corresponding samples. As the ordinary least-squares method is not able to account for measurement uncertainties in both T and C variables, an appropriate regression method is used to solve this difficulty and to evaluate correctly the uncertainty in TSS concentrations estimated from measured turbidity. The regression method is described, including detailed calculations of variances and covariance in the regression parameters. An example of application is given for a calibrated turbidimeter used in a combined sewer system, with data collected during three dry weather days. In order to show how the established regression could be used, an independent 24 hours long dry weather turbidity data series recorded at 2 min time interval is used, transformed into estimated TSS concentrations, and compared to TSS concentrations measured in samples. The comparison appears as satisfactory and suggests that turbidity measurements could replace traditional samples. Further developments, including wet weather periods and other types of sensors, are suggested.

scholarly journals Using Least squares methods and nonlinear regression Methods to Calculate the Approximate Value of Ionicity in Terms of the Energy Gap

2019 ◽  
Vol 24 (5) ◽  
pp. 97
Author(s):  
Ghassan E. Arif ◽  
Sura Y. Jaafar ◽  
, Shymaa M. Abdullah
Keyword(s):  
Regression Analysis ◽  
Numerical Analysis ◽  
Least Squares ◽  
Energy Gap ◽  
Least Squares Method ◽  
Regression Method ◽  
Quadratic Regression ◽  
Nonlinear Method ◽  
Regression Methods ◽  
Analysis Methods

The objective of the current study is to find the best mathematical models to calculate the estimated value of the ionization for the physical compounds of semiconductors based on the energy gap throughout using some numerical analysis methods as the least squares method. The best of its branches obtained is a nonlinear method of the second degree, we compare the new result with other methods and we obtained our new method is more accurate and efficiency. Another side we using some regression analysis methods as the regression method. The best of its branches obtained is a nonlinear method of the quadratic regression model.   http://dx.doi.org/10.25130/tjps.24.2019.097

Application of Robust Regression Methods to Rotor Balancing Using High Breakdown Point and Bounded-Influence Estimators

2009 ◽  
Author(s):  
Paolo Pennacchi ◽  
Andrea Vania ◽  
Steven Chatterton
Keyword(s):  
Robust Regression ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Breakdown Point ◽  
Operating Conditions ◽  
Regression Methods ◽  
Weighted Least Squares Method ◽  
High Breakdown Point ◽  
Bounded Influence ◽  
Rotor Balancing

In industrial field, the main practical problem of rotating machinery concerns rotor balancing. Balancing masses are often selected by means of weighted least squares method. The weighted method allows reducing the amplitude of vibrations at selected rotating speeds such as critical speeds or operating conditions. Usually these weights are manually selected by the operator. In this paper, an automatic procedure based on robust regression methods is introduced. In particular the analysis is focused on high breakdown point and bounded-influence estimators. Theoretical aspects and properties of these methods are investigated. The effectiveness and robustness of the proposed procedure is shown by means of simulations of a 180 MW gas turbo-generator of a power plant. Different unbalance conditions are considered as well as data corruption.

scholarly journals Three contributions to robust regression diagnostics

2015 ◽  
Vol 11 (2) ◽  
pp. 69-78 ◽  
Author(s):  
J. Kalina
Keyword(s):  
Robust Regression ◽  
Null Distribution ◽  
Real Data ◽  
Random Regression ◽  
Diagnostic Tools ◽  
Regression Diagnostics ◽  
Least Trimmed Squares ◽  
Test Statistic ◽  
Regression Methods ◽  
Regression Parameters

Abstract Robust regression methods have been developed not only as a diagnostic tool for standard least squares estimation in statistical and econometric applications, but can be also used as self-standing regression estimation procedures. Therefore, they need to be equipped by their own diagnostic tools. This paper is devoted to robust regression and presents three contributions to its diagnostic tools or estimating regression parameters under non-standard conditions. Firstly, we derive the Durbin-Watson test of independence of random regression errors for the regression median. The approach is based on the approximation to the exact null distribution of the test statistic. Secondly, we accompany the least trimmed squares estimator by a subjective criterion for selecting a suitable value of the trimming constant. Thirdly, we propose a robust version of the instrumental variables estimator. The new methods are illustrated on examples with real data and their advantages and limitations are discussed.

FAKTOR-FAKTOR YANG MEMPENGARUHI PENDAPATAN USAHATANI KACANG TANAH DI KECAMATAN SEMAU KABUPATEN KUPANG

2020 ◽  
Vol 21 (1) ◽  
pp. 25-33
Author(s):  
Deni K.L. Mudin ◽  
Paulus Un ◽  
Lika Bernadina
Keyword(s):  
Social Life ◽  
Economic Value ◽  
Coefficient Of Determination ◽  
Labor Costs ◽  
Land Area ◽  
Average Income ◽  
Dry Land ◽  
Regression Methods ◽  
The Cost ◽  
Total Average

ABSTRACT Peanuts are one of the high economic value commodities in the dry land area. This commodity also contributes to the social life of the dry land area. This research has been conducted in Semau Sub-district, Kupang Regency, with the aim to determine the amount of income, break event point (BEP), R / C ratio, efficiency of capital use and factors that affect the income of peanuts farming, with the number of farmer respondents as many as 92 people , simple randomly selected. Data that has been collected by survey, library and interview methods; analyzed quantitatively-descriptive using regression methods. The results showed that the total average income of peanut farming in the study location was IDR 1,739,895 with a total average income of IDR 3,498,261 and a total average cost of IDR 1,758,366. While the break event point average of production is 147 Kg and the break event point price is IDR. 6.509, while for the total average the R / C ratio is 1.99. With factors that affect income are production (X1), seed costs (X2), and labor costs (X3). From the regression results with the Cobb-Douglass function the coefficient of determination (R2) is 0.822 with the meaning that variations in independent variables such as production, seed costs and labor costs explain the dependent variable namely income (Y) of 82.20% and the rest 17.80 % is explained by variables outside of the variables analyzed. From the results of the F test (diversity test) it was found that the factors X1, X2, and X3 had a significant effect on income at ⍺ 1%, then accept H1 at least one of: βi ≠ 0. Whereas the results of the t test (partial test) obtained that factors significant effect on income, namely production (X1) and labor costs (X2), while the cost of seeds (X3) does not significantly affect income.

A Survey on Causal Inference

2021 ◽  
Vol 15 (5) ◽  
pp. 1-46
Author(s):  
Liuyi Yao ◽  
Zhixuan Chu ◽  
Sheng Li ◽  
Yaliang Li ◽  
Jing Gao ◽  
...  
Keyword(s):  
Machine Learning ◽  
Causal Inference ◽  
Observational Data ◽  
Causal Effect ◽  
Research Direction ◽  
Estimation Methods ◽  
Potential Outcome ◽  
Outcome Framework ◽  
Benchmark Datasets ◽  
Inference Methods

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy, and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well-known causal inference frameworks. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine, and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

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