İstatistik Bilim Dalı

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A New Estimation Technique for AR(1) Model with Long-Tailed Symmetric Innovations
(Springer, 2018) Dener Akkaya, Ayşen; Türker Bayrak, Özlem; 56416
In 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.
Effect of Estimation on Simple Linear Profile Monitoring under Non-normality
(2019) Aytaçoğlu, Burcu; Türker Bayrak, Özlem; 56416
In recent years, many control charts have been proposed to monitor profiles where the quality of a process/product is expressed as function of response and explanatory variable(s). The methods mostly assume that the in control parameter values are known in Phase II analysis and innovations are normally distributed. However, in practice, the parameters are estimated in Phase I analysis and innovations may be non-normal. In this study, the performance of T2, EWMA-R and EWMA-3 methods for monitoring simple linear profiles is examined via simulation where the parameters are estimated and innovations have Student’s t-distribution. As a performance measure, both the average and standard deviation of the run length is considered. Finally, some recommendations for practitioners are summarized in a table.
Linear Profile Monitoring Adapted to Construct Early Warning System in Economics: A Pilot Study From Energy Sector
(2019) Türker Bayrak, Özlem; Aytaçoğlu, Burcu; Yüksel Haliloğlu, Ebru; 56416
In this study, control charts for monitoring linear profiles are adopted to early warning system (EWS) to see if global crises can be detected before they occur so that preventive actions can be taken by the policy makers. For this purpose, the relation between the annual gross domestic product (GDP) and energy consumption of G8 and big emerging countries through the years 1980-2012 is observed. Phase I analysis indicated that the model parameters are autocorrelated through time. Thus, the Shewhart and EWMA charts for linear profile monitoring are adopted to take this into account and found that EWMA is better. It is seen that the 2008 global crisis can be detected whereas relatively local Asian crisis cannot. This is the first study that integrates linear profile monitoring schemes to EWS and that takes into account the correlation among profiles with different explanatory variables (x-values) for each profile.

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