An alternative algorithm of the empirical likelihood estimation for the parameter of a linear regression model

Özdemir, Şenay; Arslan, Olçay

doi:10.1080/03610918.2018.1435801

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Since the maximal estimation of computational empirical likelihood will encounter numerical calculation problems, when solving RELGEÊ β , we refer to the Newton-type algorithm of Lagrange multiplier for constrained optimization problems proposed by Özdemir (2018) [19]. In order to make the calculation simple and without loss of generality, we pull ij p , ij y , ij x and…”

Section: Algorithmmentioning

confidence: 99%

Robust Element-Wise Empirical Likelihood Estimation Method for Longitudinal Data

Huang¹,

Fan²,

Sun³

2019

JAMP

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For the regression model about longitudinal data, we combine the robust estimation equation with the elemental empirical likelihood method, and propose an efficient robust estimator, where the robust estimation equation is based on bounded scoring function and the covariate depended weight function. This method reduces the influence of outliers in response variables and covariates on parameter estimation, takes into account the correlation between data, and improves the efficiency of estimation. The simulation results show that the proposed method is robust and efficient.

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Section: Algorithmmentioning

confidence: 99%

Robust Element-Wise Empirical Likelihood Estimation Method for Longitudinal Data

Huang¹,

Fan²,

Sun³

2019

JAMP

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“…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

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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.

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Combining empirical likelihood and robust estimation methods for linear regression models

Özdemir

Arslan

2019

Communications in Statistics - Simulation and Computation

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Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional assumptions on error terms. However, these distributional assumptions on the errors may not be appropriate for some data sets. In these case, nonparametric methods may be considered to carry on the regression analysis. Empirical likelihood (EL) method is one of these nonparametric methods. The EL method maximizes a function, which is multiplication of the unknown probabilities corresponding to each observation, under some constraints inherited from the normal equations in OLS estimation method. However, it is well known that the OLS method has poor performance when there are some outliers in the data. In this paper, we consider the EL method with robustifyed constraints. The robustification of the constraints is done by using the robust M estimation methods for regression. We provide a small simulation study and a real data example to demonstrate the capability of the robust EL method to handle unusual observations in the data. The simulation and real data results reveal that robust constraints are needed when heavy tailedness and/or outliers are possible in the data.

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An alternative algorithm of the empirical likelihood estimation for the parameter of a linear regression model

Cited by 3 publications

References 14 publications

Robust Element-Wise Empirical Likelihood Estimation Method for Longitudinal Data

Robust Element-Wise Empirical Likelihood Estimation Method for Longitudinal Data

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

Combining empirical likelihood and robust estimation methods for linear regression models

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