WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Adaptive Estimation of Autoregression Models Under Long-Tailed Symmetric Distribution(Taylor & Francis inc, 2024) Yentur, Begum; Akkaya, Aysen D.; Bayrak, Ozlem TurkerNon-normal innovations in autoregression models frequently occur in practice. In this situation, least squares (LS) estimators are known to be inefficient and non-robust, and maximum likelihood (ML) estimators need to be solved numerically, which becomes a daunting task. In the literature, the modified maximum likelihood (MML) estimation technique has been proposed to obtain the estimators of model parameters. While an explicit solution can be found via this method, the requirement of knowing the shape parameter becomes a drawback, especially in machine learning. In this study, we use the adaptive modified maximum likelihood (AMML) methodology, which combines the MML with Huber's M-estimation so that this assumption is relaxed. The performance of the method in terms of efficiency and robustness is analyzed via simulation and compared to LS, MML and ML estimates that are obtained numerically via the Expectation Conditional Maximization (ECM) algorithm. Test statistics are proposed for the crucial parameters of the model. The results show that the AMML estimators are preferable in most of the settings according to the mean squared error (MSE) criterion and the test statistics based on AMML method are more robust than the others. Furthermore, both real life and synthetic data examples are given.Article Multiple linear regression model under nonnormality(Taylor & Francis Inc, 2004) Islam, M. Qamarul; Tiku, Moti L.We consider multiple linear regression models under nonnormality. We derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust. We show that the least squares esimators are considerably less efficient. We compare the efficiencies of the MMLEs and the M estimators for symmetric distributions and show that, for plausible alternatives to an assumed distribution, the former are more efficient. We provide real-life examples.Article Citation - WoS: 62Citation - Scopus: 64Multiple Linear Regression Model Under Nonnormality(Taylor & Francis inc, 2004) Islam, MQ; Tiku, MLWe consider multiple linear regression models under nonnormality. We derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust. We show that the least squares esimators are considerably less efficient. We compare the efficiencies of the MMLEs and the M estimators for symmetric distributions and show that, for plausible alternatives to an assumed distribution, the former are more efficient. We provide real-life examples.Article Citation - WoS: 27Citation - Scopus: 29Nonnormal Regression. I. Skew Distributions(Taylor & Francis inc, 2001) Islam, MQ; Tiku, ML; Yildirim, FIn a linear regression model of the type y = thetaX + e, it is often assumed that the random error e is normally distributed. In numerous situations, e.g., when y measures life times or reaction times, e typically has a skew distribution. We consider two important families of skew distributions, (a) Weibull with support IR: (0, infinity) on the real line, and (b) generalised logistic with support IR: (-infinity, infinity). Since the maximum likelihood estimators are intractable in these situations, we derive modified likelihood estimators which have explicit algebraic forms and are, therefore, easy to compute. We show that these estimators are remarkably efficient, and robust. We develop hypothesis testing procedures and give a real life example.Article Citation - WoS: 42Citation - Scopus: 47Nonnormal Regression.: Ii.: Symmetric Distributions(Taylor & Francis inc, 2001) Tiku, ML; Islam, MQ; Selçuk, ASSalient features of a family of short-tailed symmetric distributions, introduced recently by Tiku and Vaughan [1], are enunciated. Assuming the error distribution to be one of this family, the methodology of modified likelihood is used to derive MML estimators of parameters in a linear regression model. The estimators are shown to be efficient, and robust to inliers. This paper is essentially the first to achieve robustness to infers. The methodology is extended to long-tailed symmetric distributions and the resulting estimators are shown to be efficient, and robust to outliers. This paper should be read in conjunction with Islam et al. [2] who develop modified likelihood methodology for skew distributions in the context of linear regression.Article Citation - Scopus: 1Inference of Autoregressive Model With Stochastic Exogenous Variable Under Short-Tailed Symmetric Distributions(Springer international Publishing Ag, 2018) Bayrak, Ozlem Tuker; Akkaya, Aysen DenerIn classical autoregressive models, it is assumed that the disturbances are normally distributed and the exogenous variable is non-stochastic. However, in practice, short-tailed symmetric disturbances occur frequently and exogenous variable is actually stochastic. In this paper, estimation of the parameters in autoregressive models with stochastic exogenous variable and non-normal disturbances both having short-tailed symmetric distribution is considered. This is the first study in this area as known to the authors. In this situation, maximum likelihood estimation technique is problematic and requires numerical solution which may have convergence problems and can cause bias. Besides, statistical properties of the estimators can not be obtained due to non-explicit functions. It is also known that least squares estimation technique yields neither efficient nor robust estimators. Therefore, modified maximum likelihood estimation technique is utilized in this study. It is shown that the estimators are highly efficient, robust to plausible alternatives having different forms of symmetric short-tailedness in the sample and explicit functions of data overcoming the necessity of numerical solution. A real life application is also given.