Undergraduate econometric textbooks generally state the Gauss-Markov theorem as follows: Among all linear unbiased estimators, the ordinary least squares (OLS) estimator is best in the sense that it has minimum variance [Gujarati 1995; Pindyck and Rubinfeld 1997; Studenmund 1997].
In addition, the Gauss-Markov theorem should be restated as follows: For any set of sample data and for the class of linear unbiased estimators, the OLS estimator generates a set of weights formed from the observations on the independent variables that, when applied to the observations on the dependent variables, uniquely yield the smallest variance compared to any other set of weights.
An example demonstrates that other linear unbiased estimators can yield the same variance as the OLS estimator; however, the weights from such formulas are identical to the OLS weights.
According to the Gauss-Markov theorem, the least-square estimators have minimum variance among all unbiased estimators
r~ are both unbiased estimators
, it can easily be shown that:
are unbiased estimators of the particle surface area and volume, respectively.
The corresponding unbiased estimators have the same form (Eq.
Although humorous and witty, this reply should not hide the difficulty of using asymptotically unbiased estimators and interpreting the results they produce.
Unbiased estimators of the specific connectivity of X can be found in the literature when a realization of X is available in a right parallelotope Z, e.
The formulas for unbiased estimators
using intersections with randomized spatial grids follow from well established general formulas of integral geometry (Baddeley and Vedel-Jensen, 2005).
it] in the two-way random effects specification), uses the quadratic unbiased estimators
(QUE) from Swamy-Arora method.
from 20 to 80) for extracting an virtually unbiased estimator
of that parameter.