Cilt:68 Sayı:01 (2019)
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Browsing Cilt:68 Sayı:01 (2019) by Author "Arslan, Olcay"
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Item Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution(Ankara Üniversitesi, 2019-02-01) Özdemir, Şenay; Güney, Yeşim; Tuaç, Yetkin; Arslan, Olcay; İstatistik; Fen FakültesiMarshall--Olkin extended Burr XII (MOEBXII) distribution is proposed by Al-Saiari et al. (2014) to obtain a more flexible family of distributions. Some estimation methods like maximum likelihood, Bayes and M estimations are used to estimate the parameters of the MOEBXII distribution in literature. In this paper, we propose to use Maximum Lq (MLq) estimation method to find alternative estimators for the parameters of the MOEBXII distribution. We give some simulation studies and a real data example to compare the performance of the MLq estimators with the maximum likelihood and M estimators. According to our results MLq estimation method is a good alternative to the maximum likelihood and M estimation methods in the presence of outliers.Item Robust Bayesian Regression Analysis Using Ramsay-Novick Distributed Errors with Student-t Prior(Ankara Üniversitesi Fen Fakültesi, 2019-02-01) Arslan, Olcay; Çankaya, Emel; Kaya, Mutlu; İstatistik; Fen FakültesiThis paper investigates bayesian treatment of regression modelling with Ramsay - Novick (RN) distribution specifically developed for robust inferential procedures. It falls into the category of the so-called heavy-tailed distributions generally accepted as outlier resistant densities. RN is obtained by coverting the usual form of a non-robust density to a robust likelihood through the modification of its unbounded influence function. The resulting distributional form is quite complicated which is the reason for its limited applications in bayesian analyses of real problems. With the help of innovative Markov Chain Monte Carlo (MCMC) methods and softwares currently available, here we first suggested a random number generator for RN distribution. Then, we developed a robust bayesian modelling with RN distributed errors and Student-t prior. The prior with heavy-tailed properties is here chosen to provide a built-in protection against the misspecification of conflicting expert knowledge (i.e. prior robustness). This is particularly useful to avoid accusations of too much subjective bias in the prior specification. A simulation study conducted for performance assessment and a real-data application on the famously known "stack loss" data demonstrated that robust bayesian estimates with RN likelihood and heavy-tailed prior are robust against outliers in all directions and inaccurately specified priors.