İstatistik Bilim Dalı Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/4382

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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
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.
Citation - WoS: 2
Citation - Scopus: 1
Inter-Laboratory Comparison Scheme for Fuel Sector, Labkar in Turkey
(Springer, 2009) Bayrak, Ozlem Turker; Okandan, Ender; Uckardes, Hale
Fuel sector is one of the powerful sectors in Turkish industry. The implementation of a new law for regulating the fuel sector had enforced the quality control of fuels sold to public. This resulted in several accredited fuel-testing laboratories to emerge. Thus, a scheme to evaluate their proficiency in measurements became an important requirement. The inter-laboratory comparison scheme LABKAR for gasoline, diesel oil, LPG, lubricating oil and biodiesel samples have evolved to fulfill this need. In this paper, LABKAR is introduced; the results obtained from the program are analyzed and discussed. The kernel densities of the participants' results show that the use of robust mean as a consensus value is appropriate for fuel samples. Although the number of rounds is not enough to derive strict conclusions, it is seen that the performance of the scheme based on the standard deviations and coefficient of variations is improving in each round. It has been observed that the number of laboratories receiving "action" or "warning" is decreasing, which indicates that they are benefiting from the scheme.
Citation - WoS: 1
Citation - Scopus: 2
Sample Design and Allocation for Random Digit Dialling
(Springer, 2005) Ayhan, HO; Islam, MQ
Sample 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.

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