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dc.contributor.creatorO'Driscoll, Diarmuid
dc.contributor.creatorRamirez, Donald E.
dc.date.accessioned2018-12-10T12:30:21Z
dc.date.available2018-12-10T12:30:21Z
dc.date.issued2016
dc.identifier.citationO’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.issn2241-2891
dc.identifier.urihttp://hdl.handle.net/10395/2537
dc.descriptionLimitations of the least squares estimators; a teaching perspective.en_US
dc.description.abstractThe 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 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).en_US
dc.language.isoengen_US
dc.publisherAthens Institute for Education and Researchen_US
dc.rights.urihttps://www.atiner.gr/papers/STA2016-2074.pdfen_US
dc.subjectLimitationsen_US
dc.subjectLeasten_US
dc.subjectSquaresen_US
dc.subjectEstimatorsen_US
dc.subjectTeaching perspectiveen_US
dc.titleLimitations of the least squares estimators; a teaching perspectiveen_US
dc.typeConference reporten_US
dc.type.supercollectionall_mic_researchen_US
dc.description.versionNoen_US


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