Even when the residuals are not distributed normally, the OLS estimator is still the best linear unbiased estimator
, a weaker condition indicating that among all linear unbiased estimators
, OLS coefficient estimates have the smallest variance.
Thus, we see that all these acceptable estimators are asymptotically unbiased in the sense that their limit distribution as n [right arrow] [infinity] is the uniform distribution-the same as for the maximum likelihood estimators, which are the unique unbiased estimators
for the parameter p.
Yang, "On the stochastic restricted almost unbiased estimators
in linear regression model," Communications in Statistics--Simulation and Computation, vol.
Forward rates are expected to neutralize future exchange rate risk for both parties (sellers and buyers of the same currency) and, to be fair, unbiased estimators
of corresponding future spot rates.
Maximum likelihood estimation is a technique which provides efficient and in most cases unbiased estimators
. In this paper, we have applied maximum likelihood estimation for systems employing square or cross QAM signals which are undergoing slow flat Rayleigh fading.
The method of ordinary least square is widely used for regression analysis because it is much simpler than maximum likelihood parameters which are estimated by ordinary least square (OLS) gives Best Linear Unbiased Estimators
for the population mean [bar.X] = [[summation].sup.N.sub.i=1] [x.sub.i]N and pth raw moments [bar.U] = [[summation].sup.N.sub.i=1] [x.sup.p.sub.i]/N of the population are given by
This measure was chosen as it has been suggested to be appropriate for describing both biased and unbiased estimators
(Spanos, 1987) and for comparing between estimators (Jenkins & Watts, 1968).
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).
The estimation of the covariance matrix for the composite error formed by the effects and the residual (e.g., [v.sub.it] = [[delta].sub.i] + [[gamma].sub.l] + [[epsilon].sub.it] in the two-way random effects specification), uses the quadratic unbiased estimators
(QUE) from Swamy-Arora method.
The dashed-dotted line represents the nonparametric estimator of the constrained HJ-bound that is used in the existing literature whereas the solid and dashed lines represent, in the order, the new maximum likelihood and approximate unbiased estimators
of the constrained HJ-bound that we develop in this paper.