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Original Articles

Asymptotic normality of variance estimator in a heteroscedastic model with dependent errors

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Pages 351-365 | Received 11 Aug 2010, Accepted 16 Dec 2010, Published online: 26 Mar 2011

References

  • Chen , Z. J. , Liang , H. Y. and Ren , Y. F. 2003 . Strong Consistency of Estimator in Heteroscedastic Model Under NA Samples . Journal of Tongji University (Natural Science) , 31 ( 8 ) : 1001 – 1005 .
  • Doukhan , P. 1994 . Mixing: Properties and Examples , Vol. 85 , Berlin : Springer . Lecture Notes in Statistics
  • Georgiev , A. A. 1988 . Consistent Nonparametric Multiple Regression: The Fixed Design Case . Journal of Multivariate Analysis , 25 ( 1 ) : 100 – 110 .
  • Gorodetskii , V. V. 1977 . On the Strong Mixing Property for Linear Sequences . Theory of Probability and its Applications , 22 : 411 – 413 .
  • Hall , P. and Heyde , C. C. 1980 . Martingale Limit Theory and its Application , New York : Academic Press .
  • Härdle , W. , Liang , H. and Gao , J. 2000 . Partially Linear Models , Heidelberg : Physica-Verlag .
  • Liang , H. Y. and Baek , J. I. 2007 . Wavelet Estimation in Heteroscedastic Model Under Censored Samples . Acta Mathematica Sinica, English Series , 23 ( 12 ) : 2253 – 2268 .
  • Liang , H. Y. and Fan , G. L. 2009 . Berry–Esseen Type Bounds of Estimators in a Semiparametric Model with Linear Process Errors . Journal of Multivariate Analysis , 100 : 1 – 15 .
  • Liang , H. Y. and Jing , B. Y. 2005 . Asymptotic Properties for Estimates of Nonparametric Regression Models Based on Negatively Associated Sequences . Journal of Multivariate Analysis , 95 : 227 – 245 .
  • Liang , H. Y. and Qi , Y. Y. 2007 . Asymptotic Normality of Wavelet Estimator of Regression Function Under NA Assumptions . Bulletin of the Korean Mathematical Society , 44 : 247 – 257 .
  • Liang , H. Y. , Zhang , D. X. and Lu , B. X. 2004 . Wavelet Estimation in Nonparametric Model Under Martingale Difference Errors . Applied Mathematics: A Journal of Chinese Universities, Series B , 19 ( 3 ) : 302 – 310 .
  • Liebscher , E. 2001 . Estimation of the Density and the Regression Function Under Mixing Conditions . Statistics & Decisions , 19 ( 1 ) : 9 – 26 .
  • Petrov , V. V. 1995 . Limit Theorems of Probability Theory , New York : Oxford University Press .
  • Roussas , G. G. 1989 . Consistent Regression with Fixed Design Points Under Dependence Condition . Statistics & Probability Letters , 8 : 41 – 50 .
  • Roussas , G. G. , Tran , L. T. and Ioannides , D. A. 1992 . Fixed Design Regression for Time Series: Asymptotic Normality . Journal of Multivariate Analysis , 40 : 262 – 291 .
  • Volkonskii , V. A. and Rozanov , Y. A. 1959 . Some Limit Theorems for Random Functions . Theory of Probability and its Applications , 4 : 178 – 197 .
  • Wang , Q. H. 1996 . Some Convergence Properties of Weighted Kernel Estimators of Regression Function in Nonparametric Model Under Random Censorship . Acta Mathematicae Applicatae Sinica , 19 ( 3 ) : 338 – 350 .
  • Withers , C. S. 1981 . Conditions for Linear Processes to be Strong Mixing . Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete , 57 : 477 – 480 .
  • Xue , L. G. 2002 . Strong Uniform Convergence Rates of the Wavelet Estimator of Regression Function under Completed and Censored Data . Acta Mathematicae Applicatae Sinica , 25 ( 3 ) : 430 – 438 .
  • Yang , S. C. 2007 . Maximal Moment Inequality for Partial Sums of Strong Mixing Sequences and Application . Acta Mathematica Sinica, English Series , 23 : 1013 – 1024 .
  • Yang , S. C. and Li , Y. M. 2006 . Uniformly Asymptotic Normality of the Regression Weighted Estimator for Strong Mixing Samples . Acta Mathematica Sinica , 49 : 1163 – 1170 .

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