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2.4 Estimation by least squares

The Gauss-Markov theorem establishes that, under the Classical Linear Regression Model (CLRM), the least squares (LS) estimators are the Best Linear Unbiased Estimators (BLUE) of the population parameters. This theorem ensures that the LS method provides reliable estimates, possessing three crucial properties: linearity, unbiasedness, and efficiency. By adhering to the assumptions of the CLRM, practitioners can confidently use LS estimators in statistical analysis and modeling, making this theorem foundational in econometrics and statistics.

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2.4 Estimation by least squares

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  1. 2.4 Estimation by least squares Gauss-Markov theorem: given CLRM, the LS estimators will be BLUE (best-linear-unbiased-estimators) CLRM / GM: reliable estimations of the population parameters. In short, we have: • Linear • Unbiased • Efficient

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