Robust parameter estimation of regression model with AR(p) error terms

Tuaç, Yetkin; Güney, Yeşim; Şenoğlu, Birdal; Arslan, Olçay

doi:10.1080/03610918.2017.1343839

Cited by 11 publications

(6 citation statements)

References 22 publications

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“…However, since these estimating equations cannot be explicitly solved to get estimators for the unknown parameters some numerical methods should be used to compute the estimates. Among all numerical methods the estimating equations suggest a simple iteratively reweighting algorithm (IRA) to compute estimates for the unknown parameters [1,25].…”

Section: Conditional Maximum Likelihood Estimationmentioning

confidence: 99%

“…In literature, parameters of an autoregressive error term regression model are estimated using LS, ML or CML estimation methods. Some of the related papers are [1], [3], [24], [25] and [26]. In all of the mentioned papers some known distributions, such as normal or t, are assumed as the error distribution to carry on estimation of the parameters of interest in this model.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Conditional Maximum Likelihood Estimationmentioning

confidence: 99%

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

show abstract

“…In these cases, heavy-tailed distributions may be considered. In this context, [8] proposed considering the t distribution with known degrees of freedom as an alternative to the Normal distribution and applying the conditional maximum likelihood (CML) method to find the estimators of the model parameters.…”

Section: Introductionmentioning

confidence: 99%

Censored autoregressive regression models with Student-$t$ innovations

Valeriano¹,

Schumacher²,

Galarza³

et al. 2021

Preprint

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This paper proposes an algorithm to estimate the parameters of a censored linear regression model when the regression errors are autocorrelated, and the innovations follow a Student-t distribution. The Student-t distribution is widely used in statistical modeling of datasets involving errors with outliers and a more substantial possibility of extreme values. The maximum likelihood (ML) estimates are obtained throughout the SAEM algorithm [1]. This algorithm is a stochastic approximation of the EM algorithm, and it is a tool for models in which the E-step does not have an analytic form. There are also provided expressions to compute the observed Fisher information matrix [2]. The proposed model is illustrated by the analysis of a real dataset that has left-censored and missing observations. We also conducted two simulations studies to examine the asymptotic properties of the estimates and the robustness of the model.

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“…Alpuim and El-Shaarawi (2008) used the ordinary least squares (OLS) estimator under the p-order autoregressive (AR(p)) error term and the normal innovations. Tuaç et al (2018) considered linear regression model with AR(p) errors with Student's t-distribution and used conditional maximum likelihood estimation of model parameters. In (2020), Tuaç et al proposed an autoregressive regression procedure based on the skew-normal and skew-t distributions.…”

Section: Introductionmentioning

confidence: 99%