ETC2410 Lecture Notes - Lecture 4: Row And Column Spaces, Linear Map, Bias Of An Estimator
11 Nov 2018
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Etc2410 week 4: more on linear regression analysis. Properties of ols estimator: expected value of ols estimator, variance of ols, ols is blue (gauss-markov theorem) C to f: does not change the column space of x, so y does not change, must change such that x stays the same i. e. 0* + 1*(a + cx1) + 2*x2 = 0 + Estimators and their unbiasedness: estimator - formula that combines sample information and produces an estimate for parameters of interest. Variance of the ols estimator: precision of unbiased estimators is determined by how the estimates are dispersed around the mean, extra assumption of homoskedasticity i. e. error u has the same variance given any values of the explanatory variables. If this assumption fails, the model exhibits heteroskedasticity: gauss-markov theorem - under assumptions mrl. 1 to mlr. 5, (ols) is the best linear unbiased estimator (blue) of .
