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Research Article

Asymptotic properties of M estimators in classical linear models with φ-mixing random errors

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Pages 3259-3284 | Received 16 Jul 2022, Accepted 22 May 2023, Published online: 25 Jun 2023

References

  • Huber PJ. Robust regression: asymptotics, conjectures and Monte Carlo. Ann Statist. 1973;1(5):799–821.
  • Cheng CS, Li KC. The strong consistency of M-estimators in linear models. J Multivar Anal. 1984;15:91–98.
  • Chen XR, Wu YH. Strong consistency of M-estimates in linear models. J Multivar Anal. 1988;27:116–130.
  • Zhao LC. Strong consistency of M-estimates in linear model. Sci China Ser A. 2002;45:1420–1427.
  • Wu QY, Jiang YY. The strong consistency of M estimator in linear model for negatively dependent random samples. Comm Statist Theory Methods. 2011;40:476–491.
  • Wang XH, Hu SH. On the strong consistency of M-estimates in linear models for negatively superadditive dependent errors. Aust N Z J Stat. 2015;57(2):259–274.
  • Deng X, Wang XJ, Wang SJ, et al. The strong consistency of M estimator in linear models based on widely orthant dependent errors. RACSAM Rev R Acad Cienc Exactas Fís Nat Ser A Mat. 2017;111:781–796.
  • Deng X, Wang XJ. Asymptotic property of M estimator in classical linear models under dependent random errors. Methodol Comput Appl Probab. 2018;20:1069–1090.
  • Zhao LC, Rao CR, Chen XR. A note on the consistency of M-estimates in linear models. In: Stochastic processes. New York: Springer; 1993. p. 359–367.
  • He XM, Shao QM. A general bahadur representation of M estimator and its application to linear regression with nonstochastic designs. Ann Statist. 1996;24(6):2608–2630.
  • Wu WB. M-estimation of linear models with dependent errors. Ann Statist. 2007;35:495–521.
  • Fan J. Moderate deviations for M-estimators in linear models with ϕ-mixing errors. Acta Math Sin (Engl Ser). 2012;28:1275–1294.
  • Fan J, Yan A, Xiu N. Asymptotic properties for M-estimators in linear models with dependent random errors. J Stat Plan Inference. 2014;148:49–66.
  • Deng X, Wang XJ. An exponential inequality for WOD sequences and its application to M estimators in multiple linear models. Statist Papers. 2020;61:1607–1627.
  • Bai ZD, Rao CR, Wu Y. M-estimation of multivariate linear regression parameters under a convex discrepancy function. Stat Sin. 1992;2:237–254.
  • Cui H, He X, Ng KW. M-estimation for linear models with spatially-correlated errors. Stat Probab Lett. 2004;66:383–393.
  • Miao BQ, Wu Y, Liu D. Limiting behavior of recursive M-estimators in multivariate linear regression models and their asymptotic efficiencies. Acta Math Sci. 2009;29:1–11.
  • Prakasa Rao BLS. Asymptotic behavior of M-estimators for the linear model with dependent errors. Bull Inst Math Sin. 1981;9:367–375.
  • Rao CR, Zhao LC. Linear representation of M-estimates in linear models. Canad J Statist. 1992;20:359–368.
  • Yohai VJ, Maronna RA. Asymptotic behavior of M-estimators for the linear model. Ann Statist. 1979;7:258–268.
  • Dobrushin RL. The central limit theorem for non-stationary Markov chain. Theory Probab Appl. 1956;1:72–88.
  • Babu GJ, Ghosh M, Singh K. On rates of convergence to normality for φ-mixing processes. Sankhyā. 1978;40(3):278–293.
  • Utev SA. The central limit theorem for φ-mixing arrays of random variables. Theory Probab Appl. 1990;35(1):131–139.
  • Kiesel R. Strong laws and summability for φ-mixing sequences of random variables. J Theoret Probab. 1998;11(1):209–224.
  • Hu SH, Wang XJ. Large deviations for some dependent sequences. Acta Math Sci. 2008;28(2):295–300.
  • Yang WZ, Wang XJ, Li XQ, et al. Berry-Esséen bound of sample quantiles for φ-mixing random variables. J Math Anal Appl. 2012;388:451–462.
  • Shen AT, Wang XH, Ling JM. On complete convergence for non-stationary φ-mixing random variables. Comm Statist Theory Methods. 2014;43(22):4856–4866.
  • Lu DW, Song LX, Zhang T. Large deviations for sum of UEND and ϕ-mixing random variables with heavy tails. Comm Statist Theory Methods. 2016;45(7):2118–2129.
  • Deng X, Wang XJ, Wu Y. The Berry-Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors. Statist Papers. 2021;62:963–984.
  • Billingsley P. Convergence of probability measures. New York: Wiley; 1968.
  • Lu CR, Lin ZY. Limit theory for mixing dependent sequences. Beijing: Science Press of China; 1997.
  • Chen XR, Zhao LC. M-methods in linear model. Shanghai: Scientific and Technical Publishers; 1996.
  • Zhao LC, Chen XR. Asymptotic behavior of M-test statistics in linear models. J Combin Inform System Sci. 1991;16:234–248.
  • Peligrad M, Utev S. Central limit theorem for linear processes. Ann Probab. 1997;25(1):443–456.
  • Yang SC. Almost sure convergence of weighted sums of mixing sequence. J Systems Sci Math Sci. 1995;15(3):254–265.

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