İstatistik Bilim Dalı Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/4382
Browse
7 results
Search Results
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 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 - 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: 1Effect of Estimation Under Nonnormality on the Phase Ii Performance of Linear Profile Monitoring Approaches(Wiley, 2019) Aytacoglu, Burcu; Bayrak, Ozlem Turker; Türker Bayrak, ÖzlemThe number of studies about control charts proposed to monitor profiles, where the quality of a process/product is expressed as function of response and explanatory variable(s), has been increasing in recent years. However, most authors assume that the in-control parameter values are known in phase II analysis and the error terms are normally distributed. These assumptions are rarely satisfied in practice. In this study, the performance of EWMA-R, EWMA-3, and EWMA-3(d(2)) methods for monitoring simple linear profiles is examined via simulation where the in-control parameters are estimated and innovations have a Student's t distribution or gamma distribution. Instead of the average run length (ARL) and the standard deviation of run length, we used average and standard deviation of the ARL as performance measures in order to capture the sampling variation among different practitioners. It is seen that the estimation effect becomes more severe when the number of phase I profiles used in estimation decreases, as expected, and as the distribution deviates from normality to a greater extent. Besides, although the average ARL values get closer to the desired values as the amount of phase I data increases, their standard deviations remain far away from the acceptable level indicating a high practitioner-to-practitioner variability.