Schaum's Outline of Statistics and Econometrics by Dominick Salvatore & Derrick Reagle

Author:Dominick Salvatore & Derrick Reagle
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2002-11-15T00:00:00+00:00

Fig. 6-3

6.5 PROPERTIES OF ORDINARY LEAST-SQUARES ESTIMATORS

Ordinary least-squares (OLS) estimators are best linear unbiased estimators (BLUE). Lack of bias means

E() = b

so that

Bias = E() − b

Best unbiased or efficient means smallest variance. Thus OLS estimators are the best among all unbiased linear estimators [see Probs. 6.14(a) and 6.15(b)]. This is known as the Gauss-Markov theorem and represents the most important justification for using OLS.

Sometimes, a researcher may want to trade off some bias for a possibly smaller variance and minimize the mean square error, MSE (see Prob. 6.29):

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