Queens University at Kingston

HyperMetricsNotes

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F. Statistical Properties of OLS Estimates

Properties Under A0-A4

  • $E[\hat\beta] = \beta$ (OLS is unbiased)

Properties Under A0-A6

  • $Var[\hat\beta] = \sigma^2(X'X)^{-1}$
  • $\hat\beta$ is BLUE

Properties Under A0-A7

  • $\hat\beta \sim N(\beta,\sigma^2(X'X)^{-1})$
  • $\hat\sigma^2 \sim \chi^2_{N-k}$
  • $\hat\sigma^2$ is statistically independent of $\hat\beta$
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Document Last revised: 1997/1/5