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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.
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
Full Text: DOI
[1] Alpuim, T.; El-Shaarawi, A., On the efficiency of regression analysis with AR(p) errors, J Appl Stat, 35, 7, 717-737 (2008) · Zbl 1147.62364
[2] Ansley, CF, An algorithm for the exact likelihood of a mixed autoregressive-moving average process, Biometrika, 66, 1, 59-65 (1979) · Zbl 0411.62059
[3] Beach, CM; Mackinnon, JG, A maximum likelihood procedure for regression with autocorrelated errors, Econom J Econom Soc, 46, 1, 51-58 (1978) · Zbl 0373.62055
[4] Cavalieri J (2002) O método de máxima Lq-verossimilhança em modelos com erros de medição. Doctoral thesis, Federal University of São Carlos, Department of Statistics. Retrieved from https://repositorio.ufscar.br/bitstream/handle/ufscar/4554/4180.pdf?sequence=1
[5] Cochrane, D.; Orcutt, GH, Application of least square to relationship containing autocorrelated error terms, J Am Stat Assoc, 44, 245, 32-61 (1949) · Zbl 0033.08201
[6] Dogru, FZ; Bulut, YM; Arslan, O., Doubly reweighted estimators for the parameters of the multivariate t-distribution, Commun Stat Theory Methods, 47, 19, 4751-4771 (2018)
[7] Ferrari, D.; Paterlini, S., The maximum Lq-likelihood method: an application to extreme quantile estimation in finance, Methodol Comput Appl Probab, 11, 1, 3-19 (2009) · Zbl 1293.62064
[8] Ferrari D, Paterlini S (2010) Efficient and robust estimation for financial returns: an approach based on q-entropy. Available at SSRN: http://ssrn.com/abstract=1906819 or doi:10.2139/ssrn.1906819
[9] Ferrari D, Yang Y (2007) Estimation of tail probability via the maximum Lq-likelihood method. Technical report 659, School of statistics, University of Minnesota
[10] Ferrari, D.; Yang, Y., Maximum Lq-likelihood estimation, Ann Stat, 38, 2, 753-783 (2010) · Zbl 1183.62033
[11] Hampel, FR; Ronchetti, EM; Rousseeuw, PJ; Stahel, WA, Robust statistics. The approach based on influence functions (1986), New York: Wiley, New York · Zbl 0593.62027
[12] Havrda, J.; Charvát, F., Quantication method of classication processes: concept of structural entropy, Kibernetika, 3, 30-35 (1967) · Zbl 0178.22401
[13] Huang, C.; Lin, J.; Ren, YY, Testing for the shape parameter of generalized extreme value distribution based on the Lq-likelihood ratio statistic, Metrika, 76, 5, 641-671 (2013) · Zbl 1307.62136
[14] Huber, PJ; Ronchetti, EM, Robust statistics (2009), New Jersey: Wiley, New Jersey · Zbl 1276.62022
[15] Maronna, RA; Martin, RD; Yohai, VJ, Robust statistics: theory and methods (2006), Chichester: Wiley, Chichester · Zbl 1094.62040
[16] Ozdemir, S.; Güney, Y.; Tuaç, Y.; Arslan, O., Maximum Lq-likelihood estimation for the parameters of Marshall-Olkin extended burr XII distribution, Commun Fac Sci Univ Ank Ser A1 Math Stat, 68, 1, 17-34 (2019)
[17] Qin, Y.; Priebe, EC, Maximum Lq-likelihood estimation via the expectation maximization algorithm: a robust estimation of mixture models, J Am Stat Assoc, 108, 503, 914-928 (2013) · Zbl 06224976
[18] Qin, Y.; Priebe, EC, Robust hypothesis testing via Lq-likelihood, Stat Sin, 27, 1793-1813 (2017) · Zbl 1392.62058
[19] R Core Team (2017) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org
[20] Ronchetti, E., Robust model selection in regression, Stat Prob Lett, 3, 21-23 (1985)
[21] Rousseeuw, PJ; Leroy, AM, Robust regression and outlier detection (1987), New York: Wiley, New York
[22] Tsallis, C., Possible generalization of Boltzmann-Gibbs statistics, J Stat Phys, 52, 479-487 (1988) · Zbl 1082.82501
[23] Tuaç, Y.; Güney, Y.; Senoglu, B.; Arslan, O., Robust parameter estimation of regression model with AR(p) error terms, Commun Stat Simul Comput, 47, 8, 2343-2359 (2018)
[24] Tuaç, Y.; Güney, Y.; Arslan, O., Parameter estimation of regression model with AR (p) error terms based on skew distributions with EM algorithm, Soft Comput, 24, 5, 3309-3330 (2020) · Zbl 1436.62087
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