İstatistik Bilim Dalı Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/4382
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Conference Object Forecasting The Natural Gas Demand At New Locations A Case Study For Turkey(2005) Türker Bayrak, Özlem; Köksal, Gülser; Okandan, EnderConference Object A New Estimation Technique for AR(1) Model with Long-Tailed Symmetric Innovations(2017) Dener Akkaya, Ayşen; Türker Bayrak, ÖzlemIn recent years, it is seen in many time series applications that innovations are non-normal. In this situation, it is known that the least squares (LS) estimators are neither efficient nor robust and maximum likelihood (ML) estimators can only be obtained numerically which might be problematic. The estimation problem is considered newly through different distributions by the use of modified maximum likelihood (MML) estimation technique which assumes the shape parameter to be known. This becomes a drawback in machine data processing where the underlying distribution cannot be determined but assumed to be a member of a broad class of distributions. Therefore, in this study, the shape parameter is assumed to be unknown and the MML technique is combined with Huber’s estimation procedure to estimate the model parameters of autoregressive (AR) models of order 1, named as adaptive modified maximum likelihood (AMML) estimation. After the derivation of the AMML estimators, their efficiency and robustness properties are discussed through simulation study and compared with both MML and LS estimators. Besides, two test statistics for significance of the model are suggested. Both criterion and efficiency robustness properties of the test statistics are discussed, and comparisons with the corresponding MML and LS test statistics are given. Finally, the estimation procedure is generalized to AR(q) models.Conference Object Global Krizler için Doğrusal Profillere Dayalı Kontrol Şemaları ile Oluşturulan Erken Uyarı Sistemi(2015) Türker Bayrak, Özlem; Aytaçoğlu, Burcu; Yüksel Haliloğlu, EbruConference Object Citation - Scopus: 1Survey and Evaluation on Modelling of Next-Day Electricity Prices(Springer New York LLC, 2014) Bayrak, Ö.T.; Weber, G.-W.; Yıldırım, M.H.Conference Object Estimation of AR(1) Model Having Generalized Logistic Disturbances(2020) Akkaya, Ayşen; Türker Bayrak, ÖzlemNon-normality is becoming a common feature in real life applications. Using non-normal disturbances in autoregressive models induces non-linearity in the likelihood equations so that maximum likelihood estimators cannot be derived analytically. Thus, modified maximum likelihood estimation (MMLE) technique is introduced in literature to overcome this difficulty. However, this method assumes the shape parameter to be known which is not realistic in real life. Recently, for unknown shape parameter case, adaptive modified maximum likelihood estimation (AMMLE) method that combines MMLE with Huber estimation method is suggested in literature. In this study, we adopt AMMLE method to AR(1) model where the disturbances are Generalized Logistic distributed. Although Huber M-estimation is not applicable to skew distributions, the AMMLE method extends Huber type work to skew distributions. We derive the estimators and evaluate their performance in terms of efficiBook Part A New Estimation Technique for AR(1) Model with Long-Tailed Symmetric Innovations(Springer, 2018) Dener Akkaya, Ayşen; Türker Bayrak, ÖzlemIn recent years, it is seen in many time series applications that innovations are non-normal. In this situation, it is known that the least squares (LS) estimators are neither efficient nor robust and maximum likelihood (ML) estimators can only be obtained numerically which might be problematic. The estimation problem is considered newly through different distributions by the use of modified maximum likelihood (MML) estimation technique which assumes the shape parameter to be known. This becomes a drawback in machine data processing where the underlying distribution cannot be determined but assumed to be a member of a broad class of distributions. Therefore, in this study, the shape parameter is assumed to be unknown and the MML technique is combined with Huber’s estimation procedure to estimate the model parameters of autoregressive (AR) models of order 1, named as adaptive modified maximum likelihood (AMML) estimation. After the derivation of the AMML estimators, their efficiency and robustness properties are discussed through simulation study and compared with both MML and LS estimators. Besides, two test statistics for significance of the model are suggested. Both criterion and efficiency robustness properties of the test statistics are discussed, and comparisons with the corresponding MML and LS test statistics are given. Finally, the estimation procedure is generalized to AR(q) models.Conference Object Citation - Scopus: 1Adaptive Estimation of Autoregressive Models Under Long-Tailed Symmetric Distribution(Association for Computing Machinery, 2019) Yentür, B.; Bayrak, Ö.T.; Akkaya, A.D.In this paper, we consider the autoregressive models where the error term is non-normal; specifically belongs to a long-tailed symmetric distribution family since it is more relevant in practice than the normal distribution. It is known that least squares (LS) estimators are neither efficient nor robust under non-normality and maximum likelihood (ML) estimators cannot be obtained explicitly and require a numerical solution which might be problematic. In recent years, modified maximum likelihood (MML) estimation is developed to overcome these difficulties. However, this method requires that the shape parameter is known which is not realistic in machine data processing. Therefore, we use adaptive modified maximum likelihood (AMML) technique which combines MML with Huber’s estimation procedure so that the shape parameter is also estimated. After derivation of the AMML estimators, their efficiency and robustness properties are discussed through a simulation study and compared with MML and LS estimators. © 2019 Association for Computing Machinery.Article Citation - Scopus: 1Linear Contrasts in One-Way Classification Ar(1) Model With Gamma Innovations(Hacettepe Univ, Fac Sci, 2016) Senoglu, Birdal; Bayrak, Ozlem TurkerIn this study, the explicit estimators of the model parameters in oneway classification AR(1) model with gamma innovations are derived by using modified maximum likelihood (MML) methodology. We also propose a new test statistic for testing linear contrasts. Monte Carlo simulation results show that the MML estimators have higher efficiencies than the traditional least squares (LS) estimators and the proposed test has much better power and robustness properties than the normal theory test.Conference Object Citation - WoS: 22Citation - Scopus: 25Classification Models Based on Tanaka's Fuzzy Linear Regression Approach: the Case of Customer Satisfaction Modeling(Ios Press, 2010) Sekkeli, Gizem; Koksal, Gulser; Batman, Inci; Bayrak, Ozlem Turker; Batmaz, Inci; Türker Bayrak, ÖzlemFuzzy linear regression (FLR) approaches are widely used for modeling relations between variables that involve human judgments, qualitative and imprecise data. Tanaka's FLR analysis is the first one developed and widely used for this purpose. However, this method is not appropriate for classification problems, because it can only handle continuous type dependent variables rather than categorical. In this study, we propose three alternative approaches for building classification models, for a customer satisfaction survey data, based on Tanaka's FLR approach. In these models, we aim to reflect both random and fuzzy types of uncertainties in the data in different ways, and compare their performances using several classification performance measures. Thus, this study contributes to the field of fuzzy classification by developing Tanaka based classification models.Article Citation - WoS: 1Citation - Scopus: 2Sample Design and Allocation for Random Digit Dialling(Springer, 2005) Ayhan, HO; Islam, MQSample design and sample allocation methods are developed for random digit dialling in household telephone surveys. The proposed method is based on a two-way stratification of telephone numbers. A weighted probability proportional to size sample allocation technique is used, with auxiliary variables about the telephone coverage rates, within local telephone exchanges of each substrata. This makes the sampling design nearly "self-weighting" in residential numbers when the prior information is well assigned. A computer program generates random numbers for the local areas within the existing phone capacities. A simulation study has shown greater sample allocation gain by the weighted probabilities proportional to size measures over other sample allocation methods. The amount of dialling required to obtain the sample is less than for proportional allocation. A decrease is also observed on the gain in sample allocation for some methods through the increasing sample sizes.