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 [2] 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.