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