Journal of the Korean Statistical Society

  • 제25권2호
  • /
  • Pages.235-241
  • /
  • 1996
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

The Asymptotic Unbiasedness of $S^2$ in the Linear Regression Model with Dependent Errors

  • Lee, Sang-Yeol (Department of Statistics, Sookmyung Women's University, Yongsan-ku, Seoul, 140-742, Korea.) ;
  • Kim, Young-Won (This Work Was supported by Sookmyung Women`s University Research Fund in)
  • 발행 : 1996.06.01
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초록

The ordinary least squares estimator of the disturbance variance in the linear regression model with stationary errors is shown to be asymptotically unbiased when the error process has a spectral density bounded from the above and away from zero. Such error processes cover a broad class of stationary processes, including ARMA processes.

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참고문헌

  1. Time Series: Theory and Methods(2nd ed.) Brockwell, P. J.;Davis, R.
  2. The American Statistician v.40 Bias of s² in linear regression with dependent errors Dunfour, J. M.
  3. Annals of Statistics v.10 Least squares estimates in stochastic regression model with applications to stochastic regression in linear dynamic systems Lai, T. L.;Wei, C. Z.
  4. Econometrica v.45 Bounds for the bias of the least squares estimator of σ² in the case of a first-order autoregressive process (positive autocorrelation) Neudecker, H.
  5. Econometrica v.46 Bounds for the LS estimator of σ² in the case of a first-order (positive) autoregressive process when the regression contains a constant term Neudecker, H.
  6. Econometrica v.42 Bounds on the variance of regression coefficients due to heteroscedastic or autoregressive errors Sathe, S. T.;Vinod, H. D.
  7. Annals of Statistics v.9 Strong consistency of least squares estimators in regression with correlated disturbances Solo, V.
  8. Journal of Korean Statistical Society v.32 The asymptotic unbiasedness of S² in the linear regression model with moving average or particular s-th order autocorrelated disturbances Song, H. S.