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Communications in Statistics - Theory and Methods Volume 45, 2016 - Issue 11
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Original Articles

Invariance principles and almost sure central limit theorem for the error variance estimator in linear models

Yu MiaoCollege of Mathematics and Information Science, Henan Normal University, XinXiang, ChinaCorrespondence[email protected]
,
Wei-Qiang GengCollege of Mathematics and Information Science, Henan Normal University, XinXiang, China
&
Saralees NadarajahSchool of Mathematics, University of Manchester, Manchester, UK
Pages 3223-3235 | Received 16 Oct 2013, Accepted 11 Feb 2014, Published online: 28 Apr 2016

References

  • Bai, Z.D, Zhao, L.C. (1982). Berry-Esseen bounds for error variance estimates in linear models. J. China Univ. Sci. Technol. 12(3):6–15 ( in Chinese).
  • Billingsley, P. (1968). Convergence of Probability Measures. New York-London-Sydney: John Wiley & Sons, Inc.
  • Brosamler, G.A. (1988). An almost everywhere central limit theorem. Math. Proc. Cambridge Philos. Soc. 104(3):561-574.
  • Chen, X.R. (1980). Invariance principles for the estimation of the error variance. Chin. Sci. Bull. 25:81–85 ( in Chinese).
  • Csörgő, M., Szyszkowicz, B., Wang, Q.Y. (2003). Donsker’s theorem for self-normalized partial sums processes. Ann. Probab. 31(3):1228–1240.
  • Fu, K.A., Liu, W.D., Zhang, L.X. (2008). Precise asymptotics for the first moment of the error variance estimator in linear models. Appl. Math. Lett. 21(6):641–647.
  • He, Y.H. (1987). Probabilities of large deviations for error variance estimators in linear models. J. Math. (Wuhan) 7(4):351–360.
  • Kallenberg, O. (1997). Foundations of Modern Probability. Probability and its Applications. New York: Springer-Verlag.
  • Lacey, M.T., Philipp, W. (1990). A note on the almost sure central limit theorem. Statist. Probab. Lett. 9(3):201–205.
  • Lin, Z.Y., Bai, Z.D. (2010). Probability Inequalities. Beijing: Science Press Beijing, Heidelberg: Springer.
  • Lu, C.R., Qiu, J. (2005). Precise asymptotics in the estimation of the error variance in linear models. Chin. Ann. Math. Ser. A 26(1):83–92.
  • Miao, Y., Geng, W.Q., Li, N., Xiao, Q. (2014). Moderate deviation principle for the error variance estimator in linear models. Commun. Statist. Theory Meth. 43(19):4215–4222.
  • Peligrad, M., Shao, Q.M. (1995). A note on the almost sure central limit theorem for weakly dependent random variables. Statist. Probab. Lett. 22(2):131–136.
  • Schatte, P. (1988). On strong versions of the central limit theorem. Math. Nachr. 137:249–256.
  • Thrum, R. (1987). A remark on almost sure convergence of weighted sums. Probab. Theory Relat Fields 75(3):425–430.
  • Yu, H. (1988). Complete convergence for the estimation of the error variance in linear models. Appl. Math. J. Chin. Univ. 3:28–40.

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