dc.contributor.creator O'Driscoll, Diarmuid dc.contributor.creator Ramirez, Donald E. dc.date.accessioned 2018-12-10T12:30:21Z dc.date.available 2018-12-10T12:30:21Z dc.date.issued 2016 dc.identifier.citation O’Driscoll, D. and Ramirez, D.E. (2016). "Limitations of the Least Squares Estimators; A Teaching Perspective", Athens: ATINER'S Conference Paper Series, No: STA2016-2074. en_US dc.identifier.issn 2241-2891 dc.identifier.uri http://hdl.handle.net/10395/2537 dc.description Limitations of the least squares estimators; a teaching perspective. en_US dc.description.abstract 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 Var(εi) = σ2. The diagonal en_US terms of the matrix Coυ( ) are the variances of the Least Squares estimators 0 ≤ i ≤ p−1 and the Gauss-Markov Theorem states is the best linear unbiased estimator. However, the OLS solutions require that (X΄X)−1 be accurately computed and ill conditioning can lead to very unstable solutions. Tikhonov, A.N. (1943) first introduced the idea of regularisation to solve ill-posed problems by introducing additional information which constrains (bounds) the solutions. Specifically, Hoerl, A.E. (1959) added the constraint term to the least squares problem as follows: minimize ||Y – Xβ||2 subject to the constraint ||β||2 = r2 for fixed r and dubbed this procedure as ridge regression. This paper gives a brief overview of ridge regression and examines the performance of three different types of ridge estimators; namely the ridge estimators of Hoerl, A.E. (1959), the surrogate estimators of Jensen, D.R. and Ramirez, D.E. (2008) and the raise estimators of Garcia, C.B., Garcia, J. and Soto, J. (2011). dc.language.iso eng en_US dc.publisher Athens Institute for Education and Research en_US dc.rights.uri https://www.atiner.gr/papers/STA2016-2074.pdf en_US dc.subject Limitations en_US dc.subject Least en_US dc.subject Squares en_US dc.subject Estimators en_US dc.subject Teaching perspective en_US dc.title Limitations of the least squares estimators; a teaching perspective en_US dc.type Conference report en_US dc.type.supercollection all_mic_research en_US dc.description.version No en_US
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