İstatistik / Statistics https://hdl.handle.net/20.500.12619/1052 2026-04-08T19:16:22Z 2026-04-08T19:16:22Z Notes on Comparison of Covariance Matrices of BLUPs Under Linear Random-Effects Model with Its Two Subsample Models Nesrin Guler Güler, Nesrin Melek Eris Buyukkaya https://hdl.handle.net/20.500.12619/3354 2020-02-24T11:05:09Z 2019-01-01T00:00:00Z Notes on Comparison of Covariance Matrices of BLUPs Under Linear Random-Effects Model with Its Two Subsample Models Nesrin Guler; Güler, Nesrin; Melek Eris Buyukkaya A general linear random-effects model that includes both fixed and random effects, and its two subsample models are considered without making any restrictions on correlation of random effects and any full rank assumptions. Predictors of joint unknown parameter vectors under these three models have different algebraic expressions. Because of having different properties and performances under these models, it is one of the main focuses to make comparison of predictors. Covariance matrices of best linear unbiased predictors (BLUPs) of unknown parameters are used as a criterion to compare with other types predictors due to their definition of minimum covariance matrices structure. The comparison problem of covariance matrices of BLUPs under the models is considered in the study. We give a variety of equalities and inequalities in the comparison of covariance matrices of BLUPs of a general linear function of fixed effects and random effects under the models by using an approach consisting matrix rank and inertia formulas. 2019-01-01T00:00:00Z On idempotency and tripotency of linear combinations of two commuting tripotent matrices Özdemir, Halim Sarduvan, Murat Güler, Nesrin https://hdl.handle.net/20.500.12619/3353 2020-02-24T11:04:22Z 2009-01-01T00:00:00Z On idempotency and tripotency of linear combinations of two commuting tripotent matrices Özdemir, Halim; Sarduvan, Murat; Güler, Nesrin Let T-1 and T-2 be two nonzero commuting n x n tripotent matrices and c(1), c(2) two nonzero complex numbers. Necessary and sufficient conditions for the tripotency and the idempotency of c(1)T(1) + c(2)T(2) are obtained. The problems considered here have also statistical importance when c(1), c(2) are real scalars and T-1, T-2 are real symmetric matrices. (C) 2008 Elsevier Inc. All rights reserved. 2009-01-01T00:00:00Z