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Öğe On some new sequence spaces and their duals(Hindawi Limited, 2024) Barlak, DamlaIn this study, we defined some new sequence spaces using regular Tribonacci matrix. We examined some properties of these spaces such as completeness, Schauder basis. We have identified α-,β-, and γ-duals of the newly created spaces.Öğe Kernel mixed and Kernel stochastic restricted ridge predictions in the partially linear mixed measurement error models: an application to COVID-19(Taylor & Francis Ltd, 2023) Kuran, Özge; Yalaz, SeçilIn this article, we define mixed predictor and stochastic restricted ridge predictor of partially linear mixed measurement error models by taking advantage of Kernel approximation. Under matrix mean square error criterion, we make the comparison of the superiorities the linear combinations of the new defined predictors. Then we investigate the asymptotic normality characteristics and the situation of the unknown covariance matrix of measurement errors. Finally, the study is ended with a Monte Carlo simulation study and COVID-19 data application.Öğe The ridge prediction error sum of squares statistic in linear mixed models(Springer Heidelberg, 2023) Kuran, Özge; Özkale, M. RevanIn case of multicollinearity, PRESS statistics has been proposed to be used in the selection of the ridge biasing parameter of the ridge estimator which is introduced as an alternative to BLUE. This newly proposed PRESS statistic for the ridge estimator, CPRESSk, depends on the conditional ridge residual and can be computed once at a time by fitting the linear mixed model with all the observations. We also define R-RidPred(2) statistic to evaluate the predictive ability of the ridge fit. Since the PRESS statistic for the BLUE is a special CPRESSk statistic, we indirectly also give closed form solution of the PRESS statistic for the BLUE. Then, we compared the predictive performance of the linear mixed model via the statistics CPRESSk, GCV(k) and C-p by considering a real data analysis and a simulation study where the optimal ridge biaisng parameter is obtained by minimizing each statistic. The study shows that the ridge predictors improve the predictive performance of a linear mixed model over BLUE in the presence of multicollinearity and each statistic gives a different optimum ridge biasing value and they show the best predictive performance at their optimum ridge biasing values. In addition, the simulation study has shown that the intensity of variance and multicollinearity is effective in determining the optimum ridge biasing value and this optimum ridge biasing value is effective on the superiority of the predictive performance of ridge estimator over BLUE.Öğe Kernel Liu prediction approach in partially linear mixed measurement error models(Taylor and Francis Ltd., 2022) Kuran, Özge; Yalaz, SeçilIn this paper, we put forward ‘kernel Liu prediction approach’ instead of ‘kernel prediction approach’ under multicollinearity case in partially linear mixed measurement error model. We obtain the necessary and sufficient condition for the superiority of the linear combinations of the predictors in the sense of the matrix mean square error criterion and give the selection of the Liu biasing parameter via the Conceptual Prediction ((Formula presented.)) criterion. The asymptotic normality condition is examined and the unknown covariance matrix of measurement errors circumstance is derived. We study a numerical example together with a Monte Carlo simulation study to evaluate the performance of the kernel Liu prediction approach at the end of this paper.Öğe Model selection via conditional conceptual predictive statistic for mixed and stochastic restricted ridge estimators in linear mixed models(John Wiley and Sons Ltd, 2022) Özkale, M. Revan; Kuran, ÖzgeIn this article, we characterize the mixed (Formula presented.) ((Formula presented.)) and conditional stochastic restricted ridge (Formula presented.) ((Formula presented.)) statistics that depend on the expected conditional Gauss discrepancy for the purpose of selecting the most appropriate model when stochastic restrictions are appeared in linear mixed models. Under the known and unknown variance components assumptions, we define two shapes of (Formula presented.) and (Formula presented.) statistics. Then, the article is concluded with both a Monte Carlo simulation study and a real data analysis, supporting the findings of the theoretical results on the (Formula presented.) and (Formula presented.) statistics.Öğe Improvement of mixed predictors in linear mixed models(Taylor and Francis Ltd., 2021) Kuran, Özge; Özkale, M. RevanIn this paper, we introduce stochastic-restricted Liu predictors which will be defined by combining in a special way the two approaches followed in obtaining the mixed predictors and the Liu predictors in the linear mixed models. Superiorities of the linear combination of the new predictor to the Liu and mixed predictors are done in the sense of mean square error matrix criterion. Finally, numerical examples and a simulation study are done to illustrate the findings. In numerical examples, we took some arbitrary observations from the data as the prior information since we did not have historical data or additional information about the data sets. The results show that this case does the new estimator gain efficiency over the constituent estimators and provide accurate estimation and prediction of the data.Öğe Wavelet estimation in nonparametric linear mixed-effects errors in variables model(Yildiz Technical University, 2022) Yalaz, Seçil; Kuran, ÖzgeNonparametric linear mixed effects models are preferred due to overcome the restrictions of linear models which need to satisfy distributional assumptions. In these models, smoothing approaches are needed to handle nonparametric part and chosen according to the type of data. When there is a measurement error in the nonparametric part, these smoothing techniques become more complicated. In this paper, we propose wavelet approach to smooth nonparametric function under known measurement error in nonparametric linear mixed effects model and then, we predict random effects pa ra meter. Fu rt hermore, as imu lation study is done to demonstrate the theoretical findings b y c omparing w ith t he c ase i gnoring measurement error. The performances are much better for the proposed model than the no measurement error case.Öğe Henderson's method approach to Kernel prediction in partially linear mixed models(Sivas Cumhuriyet Üniversitesi Fen Fakültesi, 2020) Kuran, Özge; Yalaz, SeçilIn this article, we propose Kernel prediction in partially linear mixed models by usingHenderson's method approach. We derive the Kernel estimator and the Kernel predictor viathe mixed model equations (MMEs) of Henderson's that they give the best linear unbiasedestimation (BLUE) of the fixed effects parameters and the nonparametric functioncomputationally easier and the best linear unbiased prediction (BLUP) of the random effectsparameters as by-products. Additionally, asymptotic property of the Kernel estimator isinvestigated. A Monte Carlo simulation study is supported to illustrate the performance ofKernel prediction in partially linear mixed models and then, we finalize the article with thehelp of conclusion and discussion part to summarize the findings.Öğe Kernel ridge prediction method in partially linear mixed measurement error model(Taylor & Francis, 2022) Kuran, Özge; Yalaz, SeçilIn this article, a new kernel prediction method by using ridge regression approach is suggested to combat multicollinearity and the impacts of its existence on various views of partially linear mixed measurement error model. We derive the necessary and sufficient condition for the superiority of the linear combinations of the predictors in the sense of the matrix mean square error criterion and give the selection of the ridge biasing parameter. The asymptotic normality condition is investigated and the unknown covariance matrix of measurement errors circumstance is handled. A real data analysis together with a Monte Carlo simulation study is made to assess endorsement of the kernel ridge prediction method.Öğe Semiparametric EIV regression model with unknown errors in all variables(Bitlis Eren Üniversitesi, 2019) Yalaz, Seçil; Tez, MüjganBu makale ile değişkenleri hatalı ölçülmüş yarı parametrik kısmi doğrusal regresyon modelinde hataların yoğunlukları bilinmediğinde kullanılabilecek bir yöntem geliştirilmektedir. Bağımsız değişkenlerin hata bulaşmış iki ölçümünün mevcudiyeti tanımlamayı sağlamak için kullanılır. Bu yöntem, ölçüm hataları yoğunluklarının bilindiği varsayımına dayanan kernel dekonvolüsyon yöntemine benzetilir. Bununla birlikte, bu dekonvolüsyon yönteminde, süper düzgün hataların varlığında bir regresyon fonksiyonunun tahmin edilmesi, yakınsama oranları çok yavaş olduğu için son derece zordur. Bu durum nedeniyle, literatürde yazarlar sadece hatanın olağan düzgün dağılıma sahip olduğu durumlarda çalışmışlardır. Bu problemi Nadaraya-Watson tahmin edicisinin Fourier temsiliyle çözebiliriz, çünkü bu yöntem hem süper düzgün hem de olağan düzgün dağılımların üstesinden gelebilir. Literatürde asimptotik normallik gösteriminde de aynı düzleştirme probleminden dolayı zorluk çekilmektedir. Bu çalışma ile parametrik kısmın asimptotik normalliğinin gösterimi de sağlanabilinmiştir. Uygulama bölümünde, Monte Carlo simülasyon denemeleri ile ������������������̂ ve ������������������̂������������������ (������������������)'nin performansları incelenmiştir.Öğe Stochastic restricted Liu predictors in linear mixed models(Taylor & Francis, 2021) Kuran, Özge; Özkale, M. RevanIn this article, we propose the stochastic restricted Liu predictors by augmenting the stochastic restrictions to the linear mixed models. The Liu biasing parameter is selected via generalized cross validation (GCV) criterion. Comparisons between the stochastic restricted Liu estimators and several other estimators, namely the BLUE, the mixed and Liu estimators are made through the mean square error matrix criterion. Finally, a numerical example and a simulation study are done to show the performance of the estimators.Öğe Improving prediction by means of a two parameter approach in linear mixed models(Taylor & Francis, 2021) Kuran, Özge; Özbay, NimetIn this article, two parameter estimator and two parameter predictor are defined via the penalized log-likelihood approach in linear mixed models. The recommended approach is quite useful when there is a strong linear relationship among the variables of fixed effects design matrix. The necessary and sufficient condition for the superiority of the two parameter predictor over the best linear unbiased predictor of linear combinations of fixed and random effects in the sense of matrix mean square error criterion is examined. Additionally, to enhance the practical utility of the two parameter estimator and the two parameter predictor, we focus on the selection issue of two biasing parameters. Thus, 10 different methods for choosing the unknown biasing parameters are offered. Two real data sets are analysed to test the performance of our new two parameter approach. In addition, a comprehensive Monte Carlo simulation is performed.
