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Explain in full details, in your own words, what it means to be a BLUE estimator.

Explain in full details, in your own words, what it means to be a BLUE estimator.

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Answer #1

ANSWER:-

  • In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero, are uncorrelated and have equal variances, the best linear unbiased estimator(BLUE) of the coefficients is given by the ordinary least squares .
  • (OLS) estimator, provided it exists. Here "best" means giving the lowest variance of the estimate, as compared to other unbiased, linear estimators. The errors do not need to be normal, nor do they need to be independent and identically distributed.The requirement that the estimator be unbiased cannot be dropped, since biased estimators exist with lower variance. See, for example, the James–Stein estimato or ridge regression.
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