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Conditional maximum Lq-likelihood estimation for regression model with autoregressive error terms. (English) Zbl 1457.62264
Summary: In this article, we consider the parameter estimation of regression model with $$p$$th-order autoregressive (AR($$p$$)) error term. We use the maximum Lq-likelihood (MLq) estimation method proposed by D. Ferrari and Y. Yang [Ann. Stat. 38, No. 2, 753–783 (2010; Zbl 1183.62033)], as a robust alternative to the classical maximum likelihood (ML) estimation method to handle the outliers in the data. After exploring the MLq estimators for the parameters of interest, we provide some asymptotic properties of the resulting MLq estimators. We give a simulation study and three real data examples to illustrate the performance of the proposed estimators over the ML estimators and observe that the MLq estimators have superiority over the ML estimators when some outliers are present in the data.
##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62J05 Linear regression; mixed models 62F10 Point estimation 62F12 Asymptotic properties of parametric estimators 60F05 Central limit and other weak theorems
R; robustbase
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