Now showing items 1-9 of 9

  • 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 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 

    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 variance-covariance 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 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 

    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 ...