Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure
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 po...
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| Format: | Article |
| Language: | English |
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Çanakkale Onsekiz Mart University
2020-12-01
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| Series: | Journal of Advanced Research in Natural and Applied Sciences |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/1462765 |
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| author | Tuğba Söküt |
| author_facet | Tuğba Söküt |
| author_sort | Tuğba Söküt |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ca44c2bf5ce645f1996f04cb4dc33da1 |
| institution | Kabale University |
| issn | 2757-5195 |
| language | English |
| publishDate | 2020-12-01 |
| publisher | Çanakkale Onsekiz Mart University |
| record_format | Article |
| series | Journal of Advanced Research in Natural and Applied Sciences |
| spelling | doaj-art-ca44c2bf5ce645f1996f04cb4dc33da12025-02-05T17:58:10ZengÇanakkale Onsekiz Mart UniversityJournal of Advanced Research in Natural and Applied Sciences2757-51952020-12-016235336310.28979/jarnas.845208453Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error StructureTuğba Söküt0https://orcid.org/0000-0002-4444-1671ÇANAKKALE ONSEKİZ MART ÜNİVERSİTESİThe 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.https://dergipark.org.tr/en/download/article-file/1462765autocorrelationfirst-order autoregressive errorleveragesmulticollinearitybiased estimatorsotokorelasyonbirinci dereceden otoregresif hatakaldıraçlarçoklu iç ilişkiyanlı tahmin ediciler |
| spellingShingle | Tuğba Söküt Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure Journal of Advanced Research in Natural and Applied Sciences autocorrelation first-order autoregressive error leverages multicollinearity biased estimators otokorelasyon birinci dereceden otoregresif hata kaldıraçlar çoklu iç ilişki yanlı tahmin ediciler |
| title | Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure |
| title_full | Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure |
| title_fullStr | Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure |
| title_full_unstemmed | Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure |
| title_short | Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure |
| title_sort | identification of leverage points in principal component regression and r k class estimators with ar 1 error structure |
| topic | autocorrelation first-order autoregressive error leverages multicollinearity biased estimators otokorelasyon birinci dereceden otoregresif hata kaldıraçlar çoklu iç ilişki yanlı tahmin ediciler |
| url | https://dergipark.org.tr/en/download/article-file/1462765 |
| work_keys_str_mv | AT tugbasokut identificationofleveragepointsinprincipalcomponentregressionandrkclassestimatorswithar1errorstructure |