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.

Heteroskedastic and autoregressive consistent estimates for the multiple regression procedure and the univariate probit procedure, respectively, are obtained through the use of the Fuller-Battese random effects generalized

least squares estimator and the Butler-Moffit random effects maximum likelihood estimator.

The, the two-stage

least squares estimator [Phi] is given by

The symmetrically censored

least squares estimator [Mathematical Expression Omitted] is then obtained by

When heteroskedasticity is present, the conventional

least squares estimator leads to estimators that are not minimum variance estimators.

In Section 2 we present the model and derive an Ordinary

Least Squares estimator and the corresponding variance-covariance matrix of the vector of regression coefficients with alternative data sets.

This rule can be shown, via a complex mathematical proof, to predict property values, on average, more accurately than the

least squares estimator.

13) For instance, the three-stage

least squares estimator.

1970): "The Small Sample Properties of Simultaneous Equation Absolute Estimators vis-a-vis

Least Squares Estimators," Econometrica, 38, 742-753.

Using non-full-rank design matrices and numerous models, Monahan covers the linear least squares problem, estimability and

least squares estimators, the Gauss-Markov model, distributional theory, statistical inference, topics in testing (such as orthogonal polynomials and contrasts), variance components and mixed models, and the multivariate linear model.

Other topics addressed include asymptotic oracle properties of SCAD-penalized

least squares estimators, critical scaling of stochastic epidemic models, additive isotone regression, and Talagrand's convex hull concentration inequality.

If [Mathematical Expression Omitted] were known independently, then we would know [Mathematical Expression Omitted] and could calculate the unbiased estimators [Mathematical Expression Omitted] and [Mathematical Expression Omitted] by correcting the ordinary

least squares estimators as follows: