Further, it is well-known that the ordinary least squares estimator
(OLSE) may not be very reliable if multicollinearity exists in the linear regression model.
Many statisticians showed interest in the mathematical properties of the method; De Jong  proved that the PLS estimator is a regularized version of the ordinary least squares estimator
. The same result was later demonstrated algebraically by Goutis et al.
Ordinary least squares estimator
(OLSE) is one of the most widely used estimator for [beta], given as
Quasi-weighted least squares estimator
for data reconciliation.
The inclusion of lagged dependent variable in the list of explanatory variables introduces the specific estimation problems even the generalized least squares estimator
for the dynamic panel data models allowing cross sectional heteroscedasticity becomes biased and inconsistent.
The least squares estimator
and the maximum-likelihood estimator are widely used in propagation model-based localization problems.
We now construct the weighted secondary residuals term J as the least squares estimator
, as follows:
In addition, a confirmatory factor analysis was run on MPLUS using a weighted least squares estimator
(WLSMV) with categorical variables (Muthen & Muthen, 2010).
In fact, a single sufficiently deviating data point can cause that the least squares estimator
breaks down and generates results that are utterly unreliable and uninformative.
The corrections for heteroscedasticity and heteroscedasticity and cross correlation do not lead to a notably improved efficiency of the Least Squares estimator
. But one critical drawback is obvious: the estimated standard deviations are no reliable estimates for the true standard errors because of their dependence on the binwidth.