Comparison of iterative algorithms for parameter estimation in nonlinear regression

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, İstatistik Bölümü, Türkiye

Tezin Onay Tarihi: 2018

Öğrenci: GAMZE MUSLUOĞLU

Danışman: AYŞEN AKKAYA

Özet:

Nonlinear regression models are more common as compared to linear ones for real life cases e.g. climatology, biology, earthquake engineering, economics etc. However, nonlinear regression models are much more complex to fit and to interpret. Classical parameter estimation methods such as least squares and maximum likelihood can also be adopted to fit the model in nonlinear regression as well, but explicit solutions can not be achieved unlike linear models. At this point, iterative algorithms are utilized to solve the problem numerically. Since there is no extensive study which compiles, classifies and compares the existing methods for nonlinear parameter estimation, the objective of this study is to fill this gap. In our study, we aim to compile the methods which are used for nonlinear parameter estimation purpose and compare them with respect to several criteria such as bias, execution time, number of iterations etc. The comparison will be conducted considering different scenarios which are small vs. large sample sizes, good vs. poor initial values, normal vs. non-normal error terms, simple vs complex models (with respect to number of parameters), and robustness. Both real and simulated data are used in the comparative study.