Eliptik Regresyon Modelleri için Kayıp Fonksiyona Dayalı Önselliğin Etkisi

Abstract

Bu çalışmada eliptik konturlu hatalara sahip olan çoklu regresyon modeli ele alınmıştır. Bayesyen bakıştan, gereksiz varsayımlarda bulunmaktan kaçınmak için, ağırlık için dengeli tipteki kayıp fonksiyonuna dayalı bir önsellik altında önsellik bilgisi gözönüne alınmıştır. Bu, regresyon analizindeki muğlak öncelik bilgisiyle Bayesyen çıkarımın özüdür. Parametre uzayının boyutuyla ilgili karşılıklı ağırlığın dahil edilmesi yoluyla yarı ampirik Bayesyen büzücü tahmincilerin performansı bundan etkilenir. Tahmin edicinin büzülme faktörünün, verilerdeki aykırı değerlere ve eliptik modellerin bilinmeyen yoğunluk yaratıcı fonksiyonuna karşı dayanıklı olduğu gösterilmiştir. Son olarak, bir uygulama ile desteklenmiştir.

Keywords

• Dengeli kayıp fonksiyonu
• Eliptik konturlu dag ̆ılım
• Kayıp fonksiyona dayalı önce- lik
• Yarı-ampirik Bayes tahmin edici
• Büzücü tahmin edici

The Impact of Prior Based Loss Function for Elliptical Regression Models

Abstract

In the paper we consider a multiple regression model with elliptically contoured errors. In the Bayesian view, a prior information is taken for the weight under a prior based balanced-type loss function in order to avoid making redundant assumptions. This is the essence of the Bayesian inference with vague prior information in regression analysis. It directly impacts on the performance of the quasi empirical Bayesian shrinkage estimators through the inclusion of a reciprocal weight related to the dimension of parameter space. The shrinkage factor of the estimator is also robust to outliers and the unknown density generator of elliptical models. Finally, this result is supported by an application.

Keywords

• Balanced loss function
• Elliptically contoured distribution
• Prior based loss function
• Quasi- empirical Bayes estimator
• Shrinkage estimator

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