A robust adaptive modified maximum likelihood estimator for the linear regression model

Creative Commons License

Acitas S., Filzmoser P., ŞENOĞLU B.

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, cilt.91, sa.7, ss.1394-1414, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 91 Sayı: 7
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/00949655.2020.1856847
  • Dergi Adı: JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Business Source Elite, Business Source Premier, CAB Abstracts, Communication Abstracts, Metadex, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1394-1414
  • Anahtar Kelimeler: Adaptive modified likelihood, efficiency, leverage point, regression, robustness
  • Ankara Üniversitesi Adresli: Evet

Özet

Robust estimators are widely used in regression analysis when the normality assumption is not satisfied. One example of robust estimators for regression is adaptive modified maximum likelihood (AMML) estimators [Donmez A. Adaptive estimation and hypothesis testing methods [dissertation]. Ankara: METU; 2010]. However, they are not robust to x outliers, so-called leverage points. In this study, we propose a new estimator called robust AMML (RAMML) which is not only robust to y outliers but also to x outliers. A simulation study is carried out to compare the performance of the RAMML estimators with some existing robust estimators. The results show that the RAMML estimators are preferable in most of the settings according to the mean squared error (MSE) criterion. Two data sets taken from the literature are also analyzed to show the implementation of the RAMML estimation methodology.