Bilim dalında tamamlanan yüksek lisans tezinin bir bölümünden üretilmiştir.
It is well known that multicollinearity, which occurs among the explanatory variables, has adverse effects on the maximum likelihood estimator in the inverse Gaussian regression model. Biased estimators are proposed to cope with the multicollinearity problem in the inverse Gaussian regression model. The main interest of this article is to introduce a new biased estimator. Also, we compare newly proposed estimator with the other estimators given in the literature. We conduct a Monte Carlo simulation and provide a real data example to illustrate the performance of the proposed estimator over the maximum likelihood and Ridge estimators. As a result of the simulation study and real data example, the newly proposed estimator is superior to the other estimators used in this study.
Bu çalışmada, sayım verilerini modellemek için kullanılan Poisson regresyonmodeline alternatif olarak tanımlanan Bell regresyon modelinde çoklu iç ilişkiolması durumunda kullanılan yanlı tahmin edicilere alternatif bir tahmin ediciönerilmiştir. Bell regresyon modeli aşırı yayılım probleminin çözümü için kullanılanbir modeldir. Bell regresyon modelinin parametreleri genellikle en çok olabilirlik(EÇO) tahmin edicisi kullanılarak tahmin edilmektedir. Fakat, çoklu iç ilişkiproblemi olması durumunda EÇO tahmin edicisinin performansı düşmektedir. Busebeple, Bell Liu-tipi tahmin edicisi önerilmiştir. Önerilen Bell Liu tipi tahminedicinin performansı Bell Ridge ve Bell Liu tahmin edicileri ile Monte Carlosimülasyon çalışması yardımıyla karşılaştırılmıştır. Ayrıca, simülasyon çalışmasınadesteklemek için gerçek veri örneği verilmiştir.
Ordinary Least Squares Estimator (OLSE) is widely used to estimate parameters in regression analysis. In practice, the assumptions of regression analysis are often not met. The most common problems that break these assumptions are outliers and multicollinearity problems. As a result of these problems, OLSE loses efficiency. Therefore, alternative estimators to OLSE have been proposed to solve these problems. Robust estimators are often used to solve the outlier problem, and biased estimators are often used to solve the multicollinearity problem. These problems do not always occur individually in the real‐world dataset. Therefore, robust biased estimators are proposed for simultaneous solutions to these problems. The aim of this study is to propose Liu‐type Generalized M Estimator as an alternative to the robust biased estimators available in the literature to obtain more efficient results. This estimator gives effective results in the case of outlier and multicollinearity in both dependent and independent variables. The proposed estimator is theoretically compared with other estimators available in the literature. In addition, Monte Carlo simulation and real dataset example are performed to compare the performance of the estimator with existing estimators.
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