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Öğe Adaptation of the jackknifed ridge methods to the linear mixed models(Taylor & Francis Ltd, 2019) Ozkale, M. Revan; Kuran, OzgeThe purpose of this article is to obtain the jackknifed ridge predictors in the linear mixed models and to examine the superiorities, the linear combinations of the jackknifed ridge predictors over the ridge, principal components regression, r-k class and Henderson's predictors in terms of bias, covariance matrix and mean square error criteria. Numerical analyses are considered to illustrate the findings and a simulation study is conducted to see the performance of the jackknifed ridge predictors.Öğe A further prediction method in linear mixed models: Liu prediction(Taylor & Francis Inc, 2020) Ozkale, M. Revan; Kuran, OzgeWe propose the Liu estimator and the Liu predictor via the penalized log-likelihood approach in linear mixed models when multicollinearity is present. The necessary and sufficient conditions for the superiority of the Liu predictor over the best linear unbiased predictor and the ridge predictor of linear combinations of fixed and random effects in the sense of matrix and scalar mean square errors are examined. Furthermore, the selection of the Liu biasing parameter is given and the findings are illustrated with both a real data set and a simulation study. The study show that the Liu estimator and predictor outperform the ridge estimator and predictor and the blue and blup in the sense of mean square error for large degree of correlation and the degree of supremacy of the Liu estimator and predictor over the ridge estimator and predictor and the blue and blup increase as the Liu biasing parameter decreases.Öğe Kernel estimator and predictor of partially linear mixed-effect errors-in-variables model(Taylor & Francis Ltd, 2021) Yalaz, Secil; Kuran, OzgeThis paper considers the partially linear mixed-effect model relating a response Y to predictors (X, Z, T) with mean function X-T beta + Z(T)b + g(T) which is a combination of the linear mixed-effect model and the nonparametric smooth function. The proposed model contains an additive measurement error in X. Taavoni and Arashi (Kernel estimation in semiparametric mixed-effect longitudinal modelling. Statist Papers. 2019. Available from: https://doi.org/10.1007/s00362019-01125-8.) approximated the nonparametric function by the profile kernel method, and made use of the weighted least squares to estimate the regression coefficients when measurement error was ignored. We derive a simple modification of their estimators by correction for attenuation stems from measurement error and demonstrate that the linear parts estimator is asymptotically normal.Öğe Marginal ridge conceptual predictive model selection criterion in linear mixed models(Taylor & Francis Inc, 2021) Kuran, Ozge; Ozkale, M. RevanIn linear mixed model selection under ridge regression, we propose the model selection criteria based on conceptual predictive () statistic.The first proposed criterion is marginal ridge C-p () statistic based on the expected marginal Gauss discrepancy. An improvement of MRCp (IMRCp) statistic is then suggested and demonstrated, which is also an asymptotically unbiased estimator of the expected marginal Gauss discrepancy. Finally, a real data analysis and a Monte Carlo simulation study are given to examine the performance of the proposed criteria.Öğe A new kernel two-parameter prediction under multicollinearity in partially linear mixed measurement error model(Taylor & Francis Ltd, 2024) Yalaz, Secil; Kuran, OzgeA Partially linear mixed effects model relating a response Y to predictors $ (X,Z,T) $ (X,Z,T) with the mean function $ X<^>{T}\beta +Zb+g(T) $ XT beta+Zb+g(T) is considered in this paper. When the parametric parts' variable X are measured with additive error and there is ill-conditioned data suffering from multicollinearity, a new kernel two-parameter prediction method using the kernel ridge and Liu regression approach is suggested. The kernel two parameter estimator of beta and the predictor of b are derived by modifying the likelihood and Henderson methods. Matrix mean square error comparisons are calculated. We also demonstrate that under suitable conditions, the resulting estimator of beta is asymptotically normal. The situation with an unknown measurement error covariance matrix is handled. A Monte Carlo simulation study, together with an earthquake data example, is compiled to evaluate the effectiveness of the proposed approach at the end of the paper.Öğe The r-d class predictions in linear mixed models(Walter De Gruyter Gmbh, 2021) Kuran, OzgeIn this paper, we propose the r-d class predictors which are general predictors of the best linear unbiased predictor (BLUP), the principal components regression (PCR) and the Liu predictors in the linear mixed models. Superiorities of the linear combination of the new predictors to each of these predictors are done in the sense of the mean square error matrix criterion. Finally, numerical examples and a simulation study are done to illustrate the findings.Öğe Unifying the prediction strategies of Theil-Goldberger and Kibria-Lukman within linear mixed models(Taylor & Francis Inc, 2024) Kuran, OzgeLinear mixed models employ the best linear unbiased estimator and the best linear unbiased predictor to estimate the parameter vectors for fixed and random effects. However, due to the undesirable variance properties of the best linear unbiased estimator in the presence of multicollinearity, alternative estimators and predictors are preferred. The Theil-Goldberger's and the Kibria-Lukman's prediction approaches are commonly used for prediction under multicollinearity in linear mixed models. To address the issue of multicollinearity, this article introduces the mixed Kibria-Lukman estimator and predictor by combining these prediction approaches. To assess their effectiveness, the proposed mixed Kibria-Lukman estimator/predictor is compared with other estimators/predictors, including the best linear unbiased estimator/the best linear unbiased predictor and mixed estimators/predictors, using the matrix mean square error criterion. Furthermore, the performance of the newly defined prediction approach is demonstrated through the analysis of greenhouse gases data and a Monte-Carlo simulation study.
