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Öğe Almost unbiased Liu-type estimators in gamma regression model(Elsevier, 2022) Asar, Yasin; Korkmaz, MerveThe Liu-type estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effect of multicollinearity problem. It is known that multicollinear-ity affects the variance of the maximum likelihood estimator negatively in gamma regression model. Therefore, an almost unbiased Liu-type estimator together with a modified version of it is proposed to overcome the multicollinearity problem. The performance of the new estimators is investigated both theoretically and numerically via a Monte Carlo simulation experiment and a real data illustration. Based on the results, it is observed that the proposed estimators can bring significant improvement relative to other competitor estimators. (c) 2021 Elsevier B.V. All rights reserved.Öğe Developing a restricted two-parameter Liu-type estimator: A comparison of restricted estimators in the binary logistic regression model(Taylor & Francis Inc, 2017) Asar, Yasin; Erisoglu, Murat; Arashi, MohammadIn the context of estimating regression coefficients of an ill-conditioned binary logistic regression model, we develop a new biased estimator having two parameters for estimating the regression vector parameter when it is subjected to lie in the linear subspace restriction H = h. The matrix mean squared error and mean squared error (MSE) functions of these newly defined estimators are derived. Moreover, a method to choose the two parameters is proposed. Then, the performance of the proposed estimator is compared to that of the restricted maximum likelihood estimator and some other existing estimators in the sense of MSE via a Monte Carlo simulation study. According to the simulation results, the performance of the estimators depends on the sample size, number of explanatory variables, and degree of correlation. The superiority region of our proposed estimator is identified based on the biasing parameters, numerically. It is concluded that the new estimator is superior to the others in most of the situations considered and it is recommended to the researchers.Öğe EFFICIENCY OF THE PRINCIPAL COMPONENT LIU-TYPE ESTIMATOR IN LOGISTIC REGRESSION(Inst Nacional Estatistica-Ine, 2020) Wu, Jibo; Asar, YasinIn this paper we propose a principal component Liu-type logistic estimator by combining the principal component logistic regression estimator and Liu-type logistic estimator to overcome the multicollinearity problem. The superiority of the new estimator over some related estimators are studied under the asymptotic mean squared error matrix. A Monte Carlo simulation experiment is designed to compare the performances of the estimators using mean squared error criterion. Finally, a conclusion section is presented.Öğe Estimation in Weibull Distribution Under Progressively Typ e-I Hybrid Censored Data(Inst Nacional Estatistica-Ine, 2022) Asar, Yasin; Belaghi, Reza ArabiIn this article, we consider the estimation of unknown parameters of Weibull distribution when the lifetime data are observed in the presence of progressively typ e-I hybrid censoring scheme. The Newton-Raphson algorithm, Expectation-Maximization (EM) algorithm and Stochastic EM algorithm are utilized to derive the maximum likelihood estimates for the unknown parameters. Moreover, Bayesian estimators using Tierney-Kadane Method and Markov Chain Monte Carlo method are obtained under three different loss functions, namely, squared error loss, linear-exponential and generalized entropy loss functions. Also, the shrinkage pre-test estimators are derived. An extensive Monte Carlo simulation experiment is conducted under different schemes so that the performances of the listed estimators are compared using mean squared error, confidence interval length and coverage probabilities. Asymptotic normality and MCMC samples are used to obtain the confidence intervals and highest posterior density intervals respectively. Further, a real data example is presented to illustrate the methods. Finally, some conclusive remarks are presented.Öğe Fine spectra of triangular triple-band matrices on sequence spaces c and lp, (0 < p < 1)(Univ Osijek, Dept Mathematics, 2016) Karaisa, Ali; Asar, Yasin; Tollu, Durhasan TurgutThe purpose of this study is to determine the fine spectra of the operator for which the corresponding upper and lower triangular matrices A(r, s, t) and B(r, s, t) are on the sequence spaces c and l(p), where (0 < p < 1), respectively. Further, we obtain the approximate point spectrum, defect spectrum and compression spectrum on these spaces. Furthermore, we give the graphical representations of the spectrum of the triangular triple band matrix over the sequence spaces c and l(p).Öğe An improved and efficient biased estimation technique in logistic regression model(Taylor & Francis Inc, 2020) Asar, Yasin; Wu, JiboIn this article, we propose a new improved and efficient biased estimation method which is a modified restricted Liu-type estimator satisfying some sub-space linear restrictions in the binary logistic regression model. We study the properties of the new estimator under the mean squared error matrix criterion and our results show that under certain conditions the new estimator is superior to some other estimators. Moreover, a Monte Carlo simulation study is conducted to show the performance of the new estimator in the simulated mean squared error and predictive median squared errors sense. Finally, a real application is considered.Öğe Improved shrinkage estimators in the beta regression model with application in econometric and educational data(Springer, 2023) Belaghi, Reza Arabi; Asar, Yasin; Larsson, RolfAlthough beta regression is a very useful tool to model the continuous bounded outcome variable with some explanatory variables, however, in the presence of multicollinearity, the performance of the maximum likelihood estimates for the estimation of the parameters is poor. In this paper, we propose improved shrinkage estimators via Liu estimator to obtain more efficient estimates. Therefore, we defined linear shrinkage, pretest, shrinkage pretest, Stein and positive part Stein estimators to estimate of the parameters in the beta regression model, when some of them have not a significant effect to predict the outcome variable so that a sub-model may be sufficient. We derived the asymptotic distributional biases, variances, and then we conducted extensive Monte Carlo simulation study to obtain the performance of the proposed estimation strategy. Our results showed a great benefit of the new methodologies for practitioners specifically in the applied sciences. We concluded the paper with two real data analysis from economics and education.Öğe Inference for two Lomax populations under joint type-II censoring(Taylor & Francis Inc, 2022) Asar, Yasin; Belaghi, R. ArabiLomax distribution has been widely used in economics, business and actuarial sciences. Due to its importance, we consider the statistical inference of this model under joint type-II censoring scenario. In order to estimate the parameters, we derive the Newton-Raphson(NR) procedure and we observe that most of the times in the simulation NR algorithm does not converge. Consequently, we make use of the expectation-maximization (EM) algorithm. Moreover, Bayesian estimations are also provided based on squared error, linear-exponential and generalized entropy loss functions together with the importance sampling method due to the structure of posterior density function. In the sequel, we perform a Monte Carlo simulation experiment to compare the performances of the listed methods. Mean squared error values, averages of estimated values as well as coverage probabilities and average interval lengths are considered to compare the performances of different methods. The approximate confidence intervals, bootstrap-p and bootstrap-t confidence intervals are computed for EM estimations. Also, Bayesian coverage probabilities and credible intervals are obtained. Finally, we consider the Bladder Cancer data to illustrate the applicability of the methods covered in the paper.Öğe A jackknifed ridge estimator in probit regression model(Taylor & Francis Ltd, 2020) Asar, Yasin; Kilinc, KadriyeIn this study, the effects of multicollinearity on the maximum likelihood estimator are analyzed in the probit regression model. It is known that the near-linear dependencies in the design matrix affect the maximum likelihood estimation negatively, namely, the standard errors become so large so that the estimations are said to be inconsistent. Therefore, a new jackknifed ridge estimator is introduced as an alternative to the maximum likelihood technique and the well-known ridge estimator. The mean squared error properties of the listed estimators are investigated theoretically. In order to evaluate the performance of the estimators, a Monte Carlo simulation study is designed, and simulated mean squared error and squared bias are used as performance criteria. Finally, the benefits of the new estimator are illustrated via a real data application.Öğe L1 Correlation-Based Penalty in High-Dimensional Quantile Regression(IEEE, 2018) Yuzbasi, Bahadir; Ahmed, S. Ejaz; Asar, YasinIn this study, we propose a new method called L1 norm correlation based estimation in quantile regression in high-dimensional sparse models where the number of explanatory variables is large, may be larger than the number of observations, however, only some small subset of the predictive variables are important in explaining the dependent variable. Therefore, the importance of new method is that it addresses both grouping affect and variable selection. Monte Carlo simulations confirm that the new method compares well to the other existing regularization methods.Öğe Liu-type estimator for the gamma regression model(Taylor & Francis Inc, 2020) Algamal, Zakariya Yahya; Asar, YasinIn this paper, we propose a new biased estimator called Liu-type estimator in gamma regression models in the presence of collinearity. We also consider some other estimators such as ridge estimator and Liu estimator and conduct a Monte Carlo simulation study to compare the estimators under different designs of collinearity. Moreover, we provide a real data application to show the applicability of the new estimator. The simulations and real data results show that the proposed estimator outperforms better than other competitor estimators by yielding smaller mean squared error (MSE).Öğe Liu-type estimator in Conway-Maxwell-Poisson regression model: theory, simulation and application(Taylor & Francis Ltd, 2024) Tanis, Caner; Asar, YasinRecently, many authors have been motivated to propose a new regression estimator in the case of multicollinearity. The most well-known of these estimators are ridge, Liu and Liu-type estimators. Many studies on regression models have shown that the Liu-type estimator is a good alternative to the ridge and Liu estimators in the literature. We consider a new Liu-type estimator, an alternative to ridge and Liu estimators in Conway-Maxwell-Poisson regression model. Moreover, we study the theoretical properties of the Liu-type estimator, and we provide some theorems showing under which conditions that the Liu-type estimator is superior to the others. Since there are two parameters of the Liu-type estimator, we also propose a method to select the parameters. We designed a simulation study to demonstrate the superiority of the Liu-type estimator compared to the ridge and Liu estimators. We also evaluated the usefulness and superiority of the proposed regression estimator with a practical data example. As a result of the simulation and real-world data example, we conclude that the proposed regression estimator is superior to its competitors according to the mean square error criterion.Öğe Liu-Type Logistic Estimators with Optimal Shrinkage Parameter(Wayne State Univ Press, 2016) Asar, YasinMulticollinearity in logistic regression affects the variance of the maximum likelihood estimator negatively. In this study, Liu-type estimators are used to reduce the variance and overcome the multicollinearity by applying some existing ridge regression estimators to the case of logistic regression model. A Monte Carlo simulation is given to evaluate the performances of these estimators when the optimal shrinkage parameter is used in the Liutype estimators, along with an application of real case data.Öğe Liu-type shrinkage estimations in linear models(Taylor & Francis Ltd, 2022) Yuzbasi, Bahadir; Asar, Yasin; Ahmed, S. EjazIn this study, we present the preliminary test, Stein-type and positive part Stein-type Liu estimators in the linear models when the parameter vector beta is partitioned into two parts, namely, the main effects beta(1) and the nuisance effects beta(2) such that beta = (beta(1), beta(2)). We consider the case that a priori known or suspected set of the explanatory variables do not contribute to predict the response so that a sub-model maybe enough for this purpose. Thus, the main interest is to estimate beta(1) when beta(2) is close to zero. Therefore, we investigate the performance of the suggested estimators asymptotically and via a Monte Carlo simulation study. Moreover, we present a real data example to evaluate the relative efficiency of the suggested estimators, where we demonstrate the superiority of the proposed estimators.Öğe Modified Ridge Regression Parameters: A Comparative Monte Carlo Study(2014) Asar, Yasin; Karaibrahimoğlu, Adnan; Genç, AşırIn multiple regression analysis, the independent variables should beuncorrelated within each other. If they are highly intercorrelated, thisserious problem is called multicollinearity. There are several methodsto get rid of this problem and one of the most famous one is the ridgeregression. In this paper, we will propose some modified ridge parameters. We will compare our estimators with some estimators proposedearlier according to mean squared error (MSE) criterion. All resultsare calculated by a Monte Carlo simulation. According to simulationstudy, our estimators perform better than the others in most of thesituations in the sense of MSE.Öğe More on the restricted Liu estimator in the logistic regression model(Taylor & Francis Inc, 2017) Wu, Jibo; Asar, YasinSiray etal. proposed a restricted Liu estimator to overcome multicollinearity in the logistic regression model. They also used a Monte Carlo simulation to study the properties of the restricted Liu estimator. However, they did not present the theoretical result about the mean squared error properties of the restricted estimator compared to MLE, restricted maximum likelihood estimator (RMLE) and Liu estimator. In this article, we compare the restricted Liu estimator with MLE, RMLE and Liu estimator in the mean squared error sense and we also present a method to choose a biasing parameter. Finally, a real data example and a Monte Carlo simulation are conducted to illustrate the benefits of the restricted Liu estimator.Öğe A new biased estimation method in tobit regression: theory and application(Taylor & Francis Ltd, 2021) Asar, Yasin; Ogutcuoglu, EsraIn this study, the effects of multicollinearity on the maximum likelihood estimator are analyzed in the tobit regression model. It is known that the near-linear dependencies in the design matrix affect the maximum likelihood estimation negatively, namely, the standard errors become so large so that the estimations are said to be inconsistent. Therefore, a new biased estimator being a generalization of the well-known Liu estimator is introduced as an alternative to the maximum likelihood estimator. Mean squared error properties of the estimators are investigated theoretically. In order to evaluate the performances of the estimators, a Monte Carlo simulation study is designed and simulated mean squared error is used as a performance criterion. Finally, the benefits of the new estimator is illustrated via real data applications.Öğe New Shrinkage Parameters for the Liu-type Logistic Estimators(Taylor & Francis Inc, 2016) Asar, Yasin; Genc, AsirThe binary logistic regression is a widely used statistical method when the dependent variable has two categories. In most of the situations of logistic regression, independent variables are collinear which is called the multicollinearity problem. It is known that multicollinearity affects the variance of maximum likelihood estimator (MLE) negatively. Therefore, this article introduces new shrinkage parameters for the Liu-type estimators in the Liu (2003) in the logistic regression model defined by Huang (2012) in order to decrease the variance and overcome the problem of multicollinearity. A Monte Carlo study is designed to show the goodness of the proposed estimators over MLE in the sense of mean squared error (MSE) and mean absolute error (MAE). Moreover, a real data case is given to demonstrate the advantages of the new shrinkage parameters.Öğe A New Two-Parameter Estimator for the Poisson Regression Model(Springer International Publishing Ag, 2018) Asar, Yasin; Genc, AsirIt is known that multicollinearity affects the maximum likelihood estimator (MLE) negatively when estimating the coefficients in Poisson regression. Namely, the variance of MLE inflates and the estimations become instable. Therefore, in this article we propose a new two-parameter estimator (TPE) and some methods to estimate these two parameters for the Poisson regression model when there is multicollinearity problem. Moreover, we conduct a Monte Carlo simulation to evaluate the performance of the estimators using mean squared error (MSE) criterion. We finally consider a real data application. The simulations results show that TPE outperforms MLE in almost all the situations considered in the simulation and it has a smaller MSE and smaller standard errors than MLE in the application.Öğe A note on some new modifications of ridge estimators(Academic Publication Council, 2017) Asar, Yasin; Genc, AsirRidge estimator is an alternative to ordinary least square estimator, when there is multicollinearity problem. There are many proposed estimators in literature. In this paper, we propose some new estimators. A Monte Carlo experiment has been conducted for the comparison of the performances of the estimators. Mean squared error (MSE) is used as a performance criterion. The benefits of new estimators are illustrated using a real dataset. According to both simulation results and application, our new estimators have better performances in the sense of MSE in most of the situations.
