The Performances of Spline and Kernel Regression Estimators in Models with Correlated Errors

Year 2012, Volume: 9 Issue: 2, 20 - 28, 15.08.2012

Serdar Demir , Dursun Aydın

Abstract

It is well known that the performances of nonparametric regression estimators severely decrease in the models with correlated errors. In this paper, the performances of the cubic smoothing spline and the Nadaraya-Watson kernel estimators, which are often used for nonparametric estimation of regression function, are investigated in the models with correlated errors. For this purpose, a simulatian study is performed and the mean square errors of the estimators are compared. The simulatian results show that the Nadaraya-Watson kernel estimator performs well in small samples, while spline estimator performs well in large samples.

Keywords

Kernel estimator, Correlated errors, Cubic spline, Nadaraya-Watson

İlişkili Hatalara Sahip Modellerde Splayn ve Çekirdek Regresyon Kestiricilerinin Performansları

Abstract

Parametrik olmayan regresyon kestiricilerinin performanslarının, ilişkili hatalara sahip modellerde ciddi biçimde azaldığı iyi bilinmektedir. Bu çalışmada, regresyon fonksiyonunun parametrik olmayan kestirimi için sıkça kullanılan kübik düzleştirme splaynı ile Nadaraya-Watson çekirdek kestiricilerinin hatalı ilişkilere sahip modellerdeki performansları incelenmiştir. Bunun için bir benzetim çalışması gerçekleştirilerek elde edilen kestirimlerin hata kareler ortalamaları karşılaştırılmıştır. Benzetim sonuçlarına göre, Nadaraya-Watson çekirdek kestirisi küçük örneklemlerde iyi performans gösteriyorken, splayn kestirisi büyük örneklemlerde iyi performans göstermektedir.

Keywords

Çekirdek kestiricisi, ilişkili hatalar, Kübik splayn, Nadaraya-Watson

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