Browsing by Author "Ramirez, Donald E."
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Anomalies of the magnitude of the bias of the maximum likelihood estimator of the regression slope
O'Driscoll, Diarmuid; Ramirez, Donald E. (Athens Institute for Education and Research, 2015)The slope of the bestfit 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
O'Driscoll, Diarmuid; Ramirez, Donald E. (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
O'Driscoll, Diarmuid; Ramirez, Donald E. (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
O'Driscoll, Diarmuid; Ramirez, Donald E. (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 variancecovariance matrix Coυ( ) = σ2(X΄X)−1, where ... 
Minimizing oblique errors for robust estimating
O'Driscoll, Diarmuid; Ramirez, Donald E.; Schmitz, Rebecca (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
O'Driscoll, Diarmuid; Ramirez, Donald E. (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
O'Driscoll, Diarmuid; Ramirez, Donald E. (NEDETAS, 2011)The slope of the bestfit 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
O'Driscoll, Diarmuid; Ramirez, Donald E. (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
O'Driscoll, Diarmuid; Ramirez, Donald E. (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 ...