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FRM Part I · FRM Exam Part I · Linear Regression

Under the Gauss-Markov assumptions, which statement correctly describes the OLS estimator?

OLS has the smallest variance among all linear unbiased estimators, which is the Gauss-Markov result that it is BLUE. This requires zero-mean, homoskedastic, uncorrelated errors. It does not claim superiority over nonlinear estimators and does not require normality.

  1. AIt has the smallest variance among all estimators, linear or nonlinear
  2. BIt has the smallest variance among all linear unbiased estimatorsCorrect
  3. CIt has the smallest bias among all linear estimators, even if variance is high
  4. DIt is efficient only if the errors are normally distributed and autocorrelated

Explanation

The Gauss-Markov theorem states OLS is BLUE: best (minimum variance) among linear unbiased estimators when errors have zero mean, constant variance, and no correlation. It does not cover nonlinear estimators, and it does not require normality or autocorrelation.

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