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A Note on the Asymptotic Property of S2 in Linear Regression Model with Correlated Errors

Lee, Seung-Chun   (Department of Statistics, Hanshin UniversityUU0001517  );
  • 초록

    An asymptotic property of the ordinary least squares estimator of the disturbance variance is considered in the regression model with correlated errors. It is shown that the convergence in probability of S $^2$ is equivalent to the asymptotic unbiasedness. Beyond the assumption on the design matrix or the variance-covariance matrix of disturbances error, the result is quite general and simplify the earlier results.


  • 주제어

    convergence in probability .   convergence in L $_1$ .   uniform integrability asymptotic unbiasedness .   strictly stationary process.  

  • 참고문헌 (8)

    1. Consistency of S² in the linear regression model with correlated errors , Kramer, W.;Berghoff, S. , Empirical Economics / v.16,pp.375-377,
    2. Fuller, W. A. , Introduction to statistical time series / v.,pp.,
    3. The asymptotic unbiasedness of S² in the linear regression model with AR(1)-disturbances , Kramer, W. , Statistical Papers / v.32,pp.71-72,
    4. The asymptotic unbiasedness of S? in the linear regression model with dependent errors , Lee, S.;Kim, Y.-W. , Journal of the Korean Statistical Society / v.25,pp.235-241,
         
    5. Bounds for the bias of the least squars estimator of σ² in case of a first-order autoregressive process (positive autocorrelation) , Neudecker, H. , Econometrica / v.45,pp.1258-1262,
    6. The asymptotic unbiasedness of S² in the linear regression model with moving average or particular s -th order autocorrelated disturbances , Song, S. H. , Journal of the Korean Statistical Society / v.23,pp.33-38,
         
    7. Chung, K. L. , A course in probability theory / v.,pp.,
    8. Consistency, asymptotic unbiasedness and bounds on the bias of S² in the linear regression model with error component disturbances , Baltagi, B.;Kramer, W. , Statistical Papers / v.35,pp.28-36,

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