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

Özdemir Ş., Güney Y., Tuaç Y., Arslan O.

JOURNAL OF APPLIED STATISTICS, cilt.49, sa.9, ss.2271-2286, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 9
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/02664763.2021.1899142
  • Dergi Adı: JOURNAL OF APPLIED STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Business Source Elite, Business Source Premier, CAB Abstracts, Veterinary Science Database, zbMATH
  • Sayfa Sayıları: ss.2271-2286
  • Anahtar Kelimeler: AR(p) error terms, dependent error, empirical likelihood, linear regression
  • Ankara Üniversitesi Adresli: Evet

Özet

Linear regression models are useful statistical tools to analyze data sets in 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. If error terms are correlated the Conditional Maximum Likelihood (CML) estimation method under normality assumption is often used to estimate the parameters of interest. The CML estimation method is required a distributional assumption on error terms. However, in practice, such distributional assumptions on error terms may not be plausible. In this paper, we propose to estimate the parameters of a linear regression model with autoregressive error term using Empirical Likelihood (EL) method, which is a distribution free estimation method. A small simulation study is provided to evaluate the performance of the proposed estimation method over the CML method. The results of the simulation study show that the proposed estimators based on EL method are remarkably better than the estimators obtained from 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.