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

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Lee, Seung-Chun

• 발행 : 2003.04.01
• 12 3

#### 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.

#### 키워드

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

#### 참고문헌

1. Empirical Economics v.16 pp.375-377 Consistency of S² in the linear regression model with correlated errors Kramer, W.;Berghoff, S. https://doi.org/10.1007/BF01206283
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4. Journal of the Korean Statistical Society v.25 pp.235-241 The asymptotic unbiasedness of S？ in the linear regression model with dependent errors Lee, S.;Kim, Y.-W.
5. Econometrica v.45 pp.1258-1262 Bounds for the bias of the least squars estimator of σ² in case of a first-order autoregressive process (positive autocorrelation) Neudecker, H.
6. Journal of the Korean Statistical Society v.23 pp.33-38 The asymptotic unbiasedness of S² in the linear regression model with moving average or particular s -th order autocorrelated disturbances Song, S. H.
7. A course in probability theory Chung, K. L.
8. Statistical Papers v.35 pp.28-36 Consistency, asymptotic unbiasedness and bounds on the bias of S² in the linear regression model with error component disturbances Baltagi, B.;Kramer, W.