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Öğe A new difference-based weighted mixed Liu estimator in partially linear models(TAYLOR & FRANCIS LTD, 2018) Akdeniz, Esra; Akdeniz, Fikri; Roozbeh, MahdiIn this paper, a generalized difference-based estimator is introduced for the vector parameter beta in the partially linear model when the errors are correlated. A generalized difference-based Liu estimator is defined for the vector parameter beta. Under the linear stochastic constraint r = R beta + e, a new generalized difference-based weighted mixed Liu estimator is introduced. The performance of this estimator over the generalized difference-based weighted mixed estimator and the generalized difference-based Liu estimator in terms of the mean squared error matrix criterion is investigated. Then, a method to select the biasing parameter d and non-stochastic weight. is considered. The efficiency properties of the newestimator are illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real data set.Öğe Efficiency of the generalized difference-based liu estimators in semiparametric regression models with correlated errors(TAYLOR & FRANCIS LTD, 2015) Akdeniz, Fikri; Duran, Esra Akdeniz; Roozbeh, Mahdi; Arashi, MohammadIn this paper, a generalized difference-based estimator is introduced for the vector parameter beta in the semiparametric regression model when the errors are correlated. A generalized difference-based Liu estimator is defined for the vector parameter beta in the semiparametric regression model. Under the linear nonstochastic constraint R beta=r, the generalized restricted difference-based Liu estimator is given. The risk function for the beta(GRD)(eta) associated with weighted balanced loss function is presented. The performance of the proposed estimators is evaluated by a simulated data set.Öğe Efficiency of the generalized-difference-based weighted mixed almost unbiased two-parameter estimator in partially linear model(TAYLOR & FRANCIS INC, 2017) Akdeniz, Fikri; Roozbeh, MahdiIn this paper, a generalized difference-based estimator is introduced for the vector parameter in partially linear model when the errors are correlated. A generalized-difference-based almost unbiased two-parameter estimator is defined for the vector parameter . Under the linear stochastic constraint r = R + e, we introduce a new generalized-difference-based weighted mixed almost unbiased two-parameter estimator. The performance of this new estimator over the generalized-difference-based estimator and generalized- difference-based almost unbiased two-parameter estimator in terms of the MSEM criterion is investigated. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset.Öğe Generalized difference-based weighted mixed almost unbiased liu estimator in semiparametric regression models(2020) Akdeniz, Fikri; Roozbeh, Mahdi; Akdeniz, Esra; Khan, Naushad MamodeIn classical linear regression analysis problems, the ordinary leastsquares (OLS) estimation is the popular method to obtain the regression weights, given the essential assumptions are satisfied. However, often, in real-life studies, the response data and its associated explanatory variables do not meet the required conditions, in particular under multicollinearity, and hence results can be misleading. To overcome such problem, this paper introduces a novel generalized differencebased weighted mixed almost unbiased Liu estimator. The performance of this new estimator is evaluated against the classical estimators using the mean squared error. This is followed by an approach to select the Liu parameter and in this context, a non-stochastic weight is also considered. Monte Carlo simulation experiments are executed to assess the performance of the new estimator and subsequently,we illustrate its application to a real-life data exampleÖğe Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models(Springer New York LLC, 2017) Akdeniz, Fikri; Roozbeh, MehdiIn this paper, a generalized difference-based estimator is introduced for the vector parameter (Formula presented.) in partially linear model when the errors are correlated. A generalized difference-based almost unbiased ridge estimator is defined for the vector parameter (Formula presented.). Under the linear stochastic constraint (Formula presented.), a new generalized difference-based weighted mixed almost unbiased ridge estimator is proposed. The performance of this estimator over the generalized difference-based weighted mixed estimator, the generalized difference-based estimator, and the generalized difference-based almost unbiased ridge estimator in terms of the mean square error matrix criterion is investigated. Then, a method to select the biasing parameter k and non-stochastic weight (Formula presented.) is considered. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset.Öğe Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models(2019) Akdeniz, Fikri; Roozbeh, MahdiIn this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized difference-based almost unbiased ridge estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, a new generalized difference-based weighted mixed almost unbiased ridge estimator is proposed. The performance of this estimator over the generalized difference-based weighted mixed estimator, the generalized difference-based estimator, and the generalized differencebased almost unbiased ridge estimator in terms of the mean square error matrix criterion is investigated. Then, a method to select the biasing parameter k and nonstochastic weight ω is considered. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real datasetÖğe İstatistikte Yeni Eğilimler ve Yöntemler([TR] TÜİK, 2013) Akdeniz, FikriBu çalışmada istatistik disiplininin önemine değinilerek, istatistiksel düşünme ve veri analizi kavramları açıklanmıştır. Veriyi bilgiye dönüştürmek için veri bilimcilerin yeri vurgulanmıştır. İstatistiğin geleceği hakkında kısaca bilgi verilmiş ve ülkemiz istatistikçilerinin uluslararası yayın yapmak için düzeyli araştırmalara ağırlık vermeleri yönünde yapılması gerekenler verilmiştir.Öğe Penalized regression via the restricted bridge estimator(Springer, 2021) Yuzbasi, Bahadir; Arashi, Mohammad; Akdeniz, FikriThis article is concerned with the bridge regression, which is a special family in penalized regression with penalty function Sigma(p)(j=1) |beta(j) (q) with q > 0, in a linear model with linear restrictions. The proposed restricted bridge (RBRIDGE) estimator simultaneously estimates parameters and selects important variables when a piece of prior information about parameters are available in either low-dimensional or high-dimensional case. Using local quadratic approximation, we approximate the penalty term around a local initial values vector. The RBRIDGE estimator enjoys a closed-form expression that can be solved when q > 0. Special cases of our proposal are the restricted LASSO (q = 1), restricted RIDGE (q = 2), and restricted Elastic Net (1 < q < 2) estimators. We provide some theoretical properties of the RBRIDGE estimator for the low-dimensional case, whereas the computational aspects are given for both low- and high-dimensional cases. An extensive Monte Carlo simulation study is conducted based on different prior pieces of information. The performance of the RBRIDGE estimator is compared with some competitive penalty estimators and the ORACLE. We also consider four real-data examples analysis for comparison sake. The numerical results show that the suggested RBRIDGE estimator outperforms outstandingly when the prior is true or near exact.Öğe Restricted estimator in two seemingly unrelated regression model(unıv punjab, 2016) Erdugan, Funda; Akdeniz, FikriThis article is concerned with the estimation problem of multicollinearity in two seemingly unrelated regression (SUR) equations with linear restrictions. We propose a restricted feasible SUR estimates of the regression coefficients of this model and compare with feasible generalized least squares (FGLS) estimator and the estimator proposed by Revankar (1974) in the matrix mean square error sense. The ideas in the article are evaluated using Monte Carlo simulation.Öğe Revıvıng some geometrıc aspects of shrınkage estımatıon ın lınear models(ANKARA UNIV, FAC SCI, 2019) Akdeniz, Fikri; Özturk, FikriIt is well known that the least squares estimator is the best linear unbiased estimator of the parameter vector in a classical linear model. But, it is 'too long' as a vector and unreliable, confidence intervals are broad for some components especially in the case of multicollinearity. Shrinkage (contraction) type estimators are efficient remedial tools in order to solve problems caused by multicollinearity. In this study, we consider a class of componentwise shrunken estimators with typical members: Mayer and Willke's contraction estimator, Marquardt's principal component estimator, Hoerl and Kennard's ridge estimator, Liu's linear unified estimator and a discrete shrunken estimator. All estimators considered are "shorter" than the least squares estimator with respect to the Euclidean norm, biased, but insensitive to multicollinearity and admissible within the set of linear estimators with respect to unweighted squared error risk. Some behaviors of these estimators are illustrated geometrically by tracing their trajectories as functions of shrinkage factors in a two-dimensional parameter space.Öğe The distribution of the Liu-type estimator of the biasing parameter in elliptically contoured models(Taylor & Francıs ınc, 2017) Arashi, M.; Nadarajah, Saralees; Akdeniz, FikriWe derive the density function of the stochastic shrinkage parameters of the Liu-type estimator in elliptical models. The correctness of derivation is checked by simulations. A real data application is also provided.
