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İstatistik Bilim Dalı Yayın Koleksiyonu

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

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Browsing İstatistik Bilim Dalı Yayın Koleksiyonu by Subject "Efficiency"

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    Conference Object
    A New Estimation Technique for AR(1) Model with Long-Tailed Symmetric Innovations
    (2017) Dener Akkaya, Ayşen; Türker Bayrak, Özlem; 56416; 09.01. Ortak Dersler Bölümü; 09. Rektörlük; 01. Çankaya Üniversitesi
    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.
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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; 09.01. Ortak Dersler Bölümü; 09. Rektörlük; 01. Çankaya Üniversitesi
    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.
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    Conference Object
    Estimation of AR(1) Model Having Generalized Logistic Disturbances
    (2020) Akkaya, Ayşen; Türker Bayrak, Özlem; 56416; 09.01. Ortak Dersler Bölümü; 09. Rektörlük; 01. Çankaya Üniversitesi
    Non-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 effici