Now showing items 1-9 of 9

• #### Anomalies of the magnitude of the bias of the maximum likelihood estimator of the regression slope ﻿

(Athens Institute for Education and Research, 2015)
The slope of the best-fit line y h x x 0 1  ( )    from minimizing a function of the squared vertical and horizontal errors is the root of a polynomial of degree four which has exactly two real roots, one positive and ...
• #### Geometric view of measurement errors ﻿

(Taylor and Francis, 2011)
The slope of the best fit line from minimizing the sum of the squared oblique errors is the root of a polynomial of degree four. This geometric view of measurement errors is used to give insight into the performance of ...
• #### An investigation of the performance of five different estimators in the measurement error regression model ﻿

(Athens Institute for Education and Research, 2015)
In a comprehensive paper by Riggs et al.(1978) the authors analyse the performances of numerous estimators for the regression slope in the measurement error model with positive measurement error variances >0 0 for X and ...
• #### Limitations of the least squares estimators; a teaching perspective ﻿

(Athens Institute for Education and Research, 2016)
The standard linear regression model can be written as Y = Xβ+ε with X a full rank n × p matrix and L(ε) = N(0, σ2In). The least squares estimator is = (X΄X)−1XY with variance-covariance matrix Coυ( ) = σ2(X΄X)−1, where ...
• #### Minimizing oblique errors for robust estimating ﻿

(Irish Mathematical Society, 2008)
The slope of the best fit line from minimizing the sum of the squared oblique errors is shown to be the root of a polynomial of degree four. We introduce a median estimator for the slope and, using a case study, we show ...
• #### Mitigating collinearity in linear regression models using ridge, surrogate and raised estimators ﻿

(Cogent OA, 2016)
Collinearity in the design matrix is a frequent problem in linear regression models, for example, with economic or medical data. Previous standard procedures to mitigate the effects of collinearity included ridge regression ...
• #### Moment estimation of measurement errors ﻿

(NEDETAS, 2011)
The slope of the best-fit line from minimizing a function of the squared vertical and horizontal errors is the root of a polynomial of degree four. We use second order and fourth order moment equations to estimate the ratio ...
• #### Response surface designs using the generalized variance inflation factors ﻿

(Cogent OA, 2015)
We study response surface designs using the generalized variance inflation factors for subsets as an extension of the variance inflation factors.
• #### Revisiting some design criteria ﻿

(Athens Institute for Education and Research, 2015)
We address the problem that the A (trace) design criterion is not scale invariant and often is in disagreement with the D (determinant) design criterion. We consider the canonical moment matrix CM and use the trace of its ...