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Unbiased Estimator For Variance. The reason to avoid biases in estimates. Population variance with a known quantity that is s2. This estimator was improved in Bod et al. The number Mj of such coefficients decreases drastically as the level index j increases.
Here it is proven that this form is the unbiased estimator for variance ie that its expected value is equal to the variance itself. The number Mj of such coefficients decreases drastically as the level index j increases. A statistic used to approximate a population parameter. That rather than appears in the denominator is counterintuitive and confuses many new students. BLUEBest Linear Unbiased Estimator Best means minimum variance or smallest variance. This estimator was improved in Bod et al.
So the Gauss-Markov Theorem says that the OLS coefficient estimators βj are the best of all linear unbiased estimators of βj where best means minimum variance.
If multiple unbiased estimates of θ are available and the estimators can be averaged to reduce the variance leading to the true parameter θ as more observations are available. The observed value of the estimator. Youll be asked to show this in the homework. The purpose of this document is to explain in the clearest possible language why the n-1 is used in the formula for computing the variance of a sample. So among unbiased estimators one important goal is to find an estimator that has as small a variance as possible Amore precise goal would be to find an unbiased estimatordthat hasuniform minimum variance. If you need that to be shown as well I show that in this video.