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New influence diagnostics in ridge regression

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  • Hadi Emami
  • Mostafa Emami

Abstract

We occasionally find that a small subset of the data exerts a disproportionate influence on the fitted regression model. We would like to locate these influential points and assess their impact on the model. However, the existence of influential data is complicated by the presence of collinearity (see, e.g. [15]). In this article we develop a new influence statistic for one or a set of observations in linear regression dealing with collinearity. We show that this statistic has asymptotically normal distribution and is able to detect a subset of high ridge leverage outliers. Using this influence statistic we also show that when ridge regression is used to mitigate the effects of collinearity, the influence of some observations can be drastically modified. As an illustrative example, simulation studies and a real data set are analysed.

Suggested Citation

  • Hadi Emami & Mostafa Emami, 2016. "New influence diagnostics in ridge regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 476-489, March.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:3:p:476-489
    DOI: 10.1080/02664763.2015.1070804
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    References listed on IDEAS

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    1. Hasan Ertas & Murat Erisoglu & Selahattin Kaciranlar, 2013. "Detecting influential observations in Liu and modified Liu estimators," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1735-1745, August.
    2. Jahufer, Aboobacker & Jianbao, Chen, 2009. "Assessing global influential observations in modified ridge regression," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 513-518, February.
    3. Shi, Lei & Wang, Xueren, 1999. "Local influence in ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 341-353, September.
    4. Nedret Billor, 1999. "An application of the local influence approach to ridge regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(2), pages 177-183.
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