Abstract
In this paper, we consider the quantile linear regression models with autoregressive errors. By incorporating the expectation–maximization algorithm into the considered model, the iterative weighted least square estimators for quantile regression parameters and autoregressive parameters are derived. Finally, the proposed procedure is illustrated by simulations and a real data example.
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References
Alhamzawi R, Yu K, Benoit DF (2012) Bayesian adaptive Lasso quantile regression. Stat Model 12:279–297
Chatterjee S, Hadi AS (1988) Statistical analysis in linear regression. Wiley, New York
Cochrane D, Orcutt GH (1949) Application of least squares regression to relationships containing auto-correlated error terms. J Am Stat Assoc 44(245):32–61
Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall, New York
Fallahpour S, Ahmed SE (2014) Shrinkage estimation and variable selection in multiple regression models with random coefficient autoregressive errors. Stat Probab Lett 92(5):199–208
Geraci M, Bottai M (2007) Quantile regression for longitudinal data using the Asymmetric Laplace distribution. Biostatistics 8:140–154
Graybill FA (1961) An introduction to linear statistical models. McGraw-Hill, New York
Jiang Y, Li H (2014) Penalized weighted composite quantile regression in the linear regression model with heavy-tailed autocorrelated errors. J Korean Stat Soc 43(4):531–543
Koenker R (2005) Quantile regression. Cambridge University Press, Cambridge
Koenker R, Bassett J (1978) Regression quantiles. Econometrica 46(1):33–50
Kozumi H, Kobayashi G (2011) Gibbs sampling methods for Bayesian quantile regression. J Stat Comput Simul 81:1565–1578
Kobayashi G, Kozumi H (2013) Bayesian analysis of quantile regression for censored dynamic panel data. Comput Stat 27:359–380
Lee J, Lund R (2004) Revisiting simple linear regression with autocorrelated errors. Biometrika 91:240–245
Li G, Li Y, Tsai CL (2015) Quantile correlations and quantile autoregressive modeling. J Am Stat Assoc 110:246–261
Lim Y, Oh H (2014) Variable selection in quantile regression when the models have autoregressive errors. J Korean Stat Soc 43(4):513–530
Lin T, Pourahmadi M, Schick A (1999) Regression models with time series errors. J Time Ser Anal 20:425–433
Liu Y, Bottai M (2009) Mixed-effects models for conditional quantiles with longitudinal data. Int J Biostatistics 5(1):1–28
McKnight SD, McKean JW, Huitema BE (2000) A double bootstrap method to analyze linear models with autoregressive error terms. Psychol Methods 5(1):87–101
McNeil AJ, Frey R, Embrechts P (2005) Quantitative risk management: concepts, techniques and tools. Princeton University Press, Princeton
Oakes D (1999) Direct calculation of the information matrix via the EM algorithm. J R Stat Soc Ser B 61(1):479–482
Ramanathan R (1998) Introductory econometrics with applications. Harcourt Brace Jovanovich, Orlando
Rao CR (1973) Linear statistical inference and its applications, 2nd edn. Wiley, New York
Rao CR, Toutenburg H, Shalabh, Heumann C (2008) Linear models and generalizations: least squares and alternatives, 3rd edn. Springer, New York
Reed C, Yu K (2009) Efficient Gibbs sampling for Bayesian quantile regression. Technical report, Brunel University, UK
Reich BJ, Fuentes M, Dunson DB (2011) Bayesian spatial quantile regression. J Am Stat Assoc 106:6–20
Rosadi D, Filzmoser P (2016) Robust second-order least-squares estimation for regression models with autoregressive errors. Stat Pap. https://doi.org/10.1007/s00362-016-0829-9
Rosadi D, Peiris S (2015) Second-order least-squares estimation for regression models with autocorrelated errors. Comput Stat 29(5):931–943
Tian YZ, Tian MZ, Zhu QQ (2014) Linear quantile regression based on EM algorithm. Commun Stat Theory Methods 43(16):3464–3484
Tian YZ, Li EQ, Tian MZ (2016) Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates. Comput Stat 31(3):1031–1057
Wu R, Wang Q (2012) Shrinkage estimation for linear regression with ARMA errors. J Stat Plan Inference 142(7):2136–2148
Yang CY (2012) Estimation of linear regression models with serially correlated errors. J Data Sci 10(4):723–755
Yoon Y-J, Park C, Lee T (2013) Penalized regression models with autoregressive error terms. J Stat Comput Simul 83(9):1756–1772
Yu K, Moyeed RA (2001) Bayesian quantile regression. Stat Probab Lett 54:437–447
Zhao KF, Lian H (2015) Bayesian Tobit quantile regression with single-index models. J Stat Comput Simul 85(6):1247–1263
Acknowledgements
The authors thank editors and two reviewers for their constructive comments and valuable suggestions which have greatly improved the paper. The work is partly supported by Young academic leaders project of Henan University of Science and Technology (No. 13490008), National Natural Science Foundation of China (No. 11501167) and China Postdoctoral Science Foundation (No. 2017M610156).
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Tian, Y., Tang, M., Zang, Y. et al. Quantile regression for linear models with autoregressive errors using EM algorithm. Comput Stat 33, 1605–1625 (2018). https://doi.org/10.1007/s00180-018-0811-1
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DOI: https://doi.org/10.1007/s00180-018-0811-1