Identification of Leverage Points in Principal Component Regression and r −k Class Estimators with AR(1) Error Structure


Söküt Açar T.

Journal of Advanced Research in Natural and Applied Sciences, cilt.6, sa.2, ss.353-363, 2020 (Hakemli Üniversite Dergisi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Konu: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.28979/jarnas.845208
  • Dergi Adı: Journal of Advanced Research in Natural and Applied Sciences
  • Sayfa Sayıları: ss.353-363

Özet

The determination of leverage observations have been frequently investigated through ordinary least squares and some biased estimators proposed under the multicollinearity problem in the linear regression models. Recently, the identification of leverage and influential observations have been also popular on the general linear regression models with correlated error structure. This paper proposes a new projection matrix and a new quasiprojection matrix to determination of leverage observations for principal component regression and r-k class estimators, respectively, in general linear regression model with first-order autoregressive error structure. Some useful properties of these matrices are presented. Leverage observations obtained by generalized least squares and ridge regression estimators available in the literature have been compared with proposed principal component regression and r-k class estimators over a simulation study and a numerical example. In the literature, the first leverage is considered separately due to the first-order autoregressive error structure. Therefore, the behaviours of first leverages obtained by principal component regression and r-k class estimators has been also investigated according to the autocorrelation coefficient and biasing parameter through applications. The results showed that the leverage of the first observation obtained by principal component regression and r-k estimators is smaller than that obtained by generalized least squares and ridge regression estimators. In addition, as the autocorrelation coefficient goes to -1, the leverage of the first transformed observation decreases for PCR and r-k class estimators, while its increases while the autocorrelation coefficient goes to 1.