Combining empirical likelihood and robust estimation methods for linear regression models

Özdemir, Şenay; Arslan, Olçay

doi:10.1080/03610918.2019.1659968

Cited by 4 publications

(3 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To address the above issues, this paper proposes the "support vector" theory for water pollution control planning and decision-making. A support vector is a mathematical model consisting of parameter functions with vectorial significance, which mainly includes regression functions, multiple linear regression and mathematical equations [7][8]. Improvements to the model are required for a given target situation.…”

Section: Problems With Water Pollution Prevention and Controlmentioning

confidence: 99%

Linear Regression for Water Pollution Control Planning under Support Vectors

2021

WPPCP

View full text Add to dashboard Cite

China is facing a serious situation in water pollution prevention and control, and the uncertainty of regional development should be fully considered when formulating water pollution prevention and control planning, and its scientificity should be improved through effective mathematical methods. Water resources and water environment are closely related to human health, and China has not yet established a comprehensive set of water resources and environment monitoring network, so the water pollution prevention and control planning process is crucial to the implementation of water pollution control planning. Due to the relatively low level of economic development in China, the state attaches less importance to water pollution prevention and control issues, and therefore also has a certain impact on the water environment. In order to reduce the problems caused by water pollution, the Water Resources Management Committee has organised the preparation of water pollution control plans. This paper presents an empirical analysis of the support vector model for water pollution prevention and control planning in China. The results of the study show that the introduction of the support vector approach to water pollution prevention and control planning in China can effectively improve the scientific nature of the planning. This paper firstly introduces the support vector model, which is a multivariate model designed based on the support vector method, and can be used to analyse multiple indicators and conduct comprehensive analysis in the prediction process; finally, the planning scheme should be designed with full consideration of water pollution prevention and control planning to avoid conflicts between different water resources and environmental issues. However, there are many problems with the use of the support vector approach in water pollution prevention and control planning that warrant further research.

show abstract

Section: Problems With Water Pollution Prevention and Controlmentioning

confidence: 99%

Linear Regression for Water Pollution Control Planning under Support Vectors

2021

WPPCP

View full text Add to dashboard Cite

show abstract

“…In fact, according to Raymaekers and Rousseeuw in [5,6] Pearson correlation is very susceptible to outliers/anomalies data. The Ordinary Least Squares (OLS) method in regression is known to have poor performance if there are outliers in the data [7].…”

Section: Introductionmentioning

confidence: 99%

The Outliers Influence on Adequateness of Classical and Robust Path Analysis

Lestari,

Kurnia,

Wigena

et al. 2024

AJOMCOR

View full text Add to dashboard Cite

Path analysis is formed from correlation and regression analysis which assumes a normal distribution. This assumption will be disturbed if there are outliers. This research aims to examine the influence of outliers on classical path analysis and robust path analysis. The data used as initial data is secondary data from Badan Pusat Statistik (BPS) publications on Indikator Kesejahteraan Rakyat, Statistik Ketenagakerjaan, Statistik Indonesia, and Survei Sosial Ekonomi Nasional. These data are used to generate data with a simulation scheme for the number of samples or n (20, 30, and 100), percentage of outliers or p (5%, 25% and 45%) and program repetitions or u (25, 50, 75, 100, 500 and 1000). Based on the combination of 3 treatments, the percentage of model adequateness was measured based on the Wald test and then an ANOVA test was carried out with 2-factor factorial design. The percentage of model adequateness of the classical path analysis model is decreasing as the number of samples increasing. In large sample sizes data, the adequateness tends to be different and increases as the percentage of outliers in the sample size data increases. The adequateness of the robust path analysis model is relatively very stable. The robust path analysis is adequate to use on small or large sample data with any percentage of outliers. The percentage of model adequateness being higher at the larger percentage of outliers. The classical path analysis model is influenced by outliers but the robust path analysis model is not influenced by outliers.

show abstract

“…Hall and La Scala [10] studied on main features of the EL, Kolaczyk [11] adapted it in generalized linear regression model,Qin and Lawless [23] combined general estimating equations and the EL, Chen et al [5][6][7][8][9] considered this method for constructing confidence regions and parameter estimation with additional constraints,Newey and Smith [13] studied higher-order properties generalized methods of moments and generalized empirical likelihood estimators, Shi and Lau [22] considered for robustifying the constraint in equation ( 5) using median constraint, and Bondell and Stefanski [4] suggested a robust estimator by maximizing a generalized EL function instead of the EL function given in equation (3). Recently, Özdemir and Arslan [20] have considered using constraints based on robust M estimation in EL estimation method. Also, Özdemir and Arslan [19] have proposed an alternative algorithm to compute EL estimators.…”

Section: Introductionmentioning

confidence: 99%

Empirical likelihood estimation for linear regression models with AR(p) error terms with numerical examples

Özdemir

Güney

Tuaç

et al. 2021

Journal of Applied Statistics

Self Cite

View full text Add to dashboard Cite

Linear regression models are useful statistical tools to analyze data sets in several different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally distributed and uncorrelated errors with zero mean and constant variance. However, for some data sets error terms may not satisfy these or some of these assumptions. If error terms are correlated, such as the regression models with autoregressive (AR(p)) error terms, the Conditional Maximum Likelihood (CML) under normality assumption or the Least Square (LS) methods are often used to estimate the parameters of interest. For CML estimation a distributional assumption on error terms is needed to carry on estimation, but, in practice, such distributional assumptions on error terms may not be plausible. Therefore, in such cases some alternative distribution free methods are needed to conduct the parameter estimation. In this paper, we propose to estimate the parameters of a linear regression model with AR(p) error term using the Empirical Likelihood (EL) method, which is one of the distribution free estimation methods. A small simulation study and a numerical example are provided to evaluate the performance of the proposed estimation method over the CML method. The results of simulation study show that the proposed estimators based on EL method are remarkably better than the estimators obtained from the CML method in terms of mean squared errors (MSE) and bias in almost all the simulation configurations. These findings are also confirmed by the results of the numerical and real data examples.

show abstract

Combining empirical likelihood and robust estimation methods for linear regression models

Cited by 4 publications

References 21 publications

Linear Regression for Water Pollution Control Planning under Support Vectors

Linear Regression for Water Pollution Control Planning under Support Vectors

The Outliers Influence on Adequateness of Classical and Robust Path Analysis

Empirical likelihood estimation for linear regression models with AR(p) error terms with numerical examples

Contact Info

Product

Resources

About