The example provided in Table 2 clearly demonstrates that despite being the best linear unbiased estimator
of the conditional expectation function from a purely statistical standpoint, naively using OLS can lead to incorrect economic inferences when there are multivariate outliers in the data.
Under this set of assumptions, [F.sub.O,T], is an unbiased estimator
of the expected future spot rate at time t.
The error variance associated with the OK estimate is called the minimum variance unbiased estimator
or best linear unbiased estimator
, since the constraint condition defined in (3) should be applied to minimize the variance of estimate errors.
Cramer-Rao Lower Bound (CRLB) is one such bound on the variance of an unbiased estimator
. When an estimator does not have any bias, the lowest possible variance it can achieve is given by the CRLB.
An estimator is optimal if it attains the Cramer-Rao Lower Bound; thus it has minimum variance, is unbiased and it is impossible to find an unbiased estimator
with a lower variance  (p.
Which was unbiased estimator
of the population variance:
The usual unbiased estimator
for population mean Y of the study variable is, given by
Also, if 6 is multivariate normal with mean 0 and variance [[sigma].sup.2]I then [[beta].sub.LSE] is the uniformly minimum variance unbiased estimator
(UMVUE) for [beta] (Graybill, 1976).
Kriging algorithms (Krige, 1951) are described as a best linear unbiased estimator
(BLUE), which is a process of a theoretical weighted moving average:
For example, [[??].sub.OLS] is the best linear unbiased estimator
of [beta] and also the maximum-likelihood estimator of [beta].
The MLEs were based on Fast Fourier Transform (FFT) implementation and the ad hoc method was based on best linear unbiased estimator
An unbiased estimator
of the wavelet variance is formed by removing all the coefficients that are affected by the boundary conditions and is given by