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Influence Diagnostics for a Class of Biased Estimators in Regression

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Computing Science and Statistics

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Abstract

Fractional Principal Components (FPC) is a large class of estimators that include, among others, least squares (LS), ridge, principal components, fractional rank, and Stein estimators. This paper addresses the measurement of influence for FPC estimators. It is shown that the residual and the leverage of any observation depends directly on the “fraction” of the principal components that is used. Generalizations of popular measures of influence for LS are proposed. Approximate deletion formulas are presented.

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References

  • Belsley, D. A., Kuh, E. and Welsch, R. E. (1980) Regression Diagnostics, Wiley, NY.

    Book  MATH  Google Scholar 

  • Cook, R. D. and Weisberg, S. (1982) Residuals and Influence in Regression, Chapman and Hall, NY.

    MATH  Google Scholar 

  • Hocking, R. R., Speed, F. M. and Lynn, M. J. (1976) A Class of Biased Estimators in Linear Regression, Technometrics, 18, 425–437.

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  • Lee, W. and Birch, J. B. (1988) Fractional Principal Components Regression: A General Approach to Biased Estimators, Communications in Statistics, Simulation and Computation, 17, 713–727.

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  • Mason, R. L. and Gunst, R. F. (1985) Outlier-Induced Collinearities, Technometrics, 27, 401–407.

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  • Walker, E. and Birch, J. B. (1988) Influence Measures in Ridge Regression, Technometrics, 30, 21–27.

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  • Walker, E. (1990) Influence Diagnostics for Fractional Principal Components Estimators, Communications in Statistics, Simulation and Computation, 19(3), 919–933.

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Author information

Authors and Affiliations

  1. Dept. of Statistics, U. of Tennessee, Knoxville, TN, 37996-0532, USA

    Esteban Walker

Authors
  1. Esteban Walker
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Editor information

Editors and Affiliations

  1. Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824, USA

    Connie Page  & Raoul LePage  & 

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© 1992 Springer-Verlag New York, Inc.

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Walker, E. (1992). Influence Diagnostics for a Class of Biased Estimators in Regression. In: Page, C., LePage, R. (eds) Computing Science and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2856-1_98

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  • DOI: https://doi.org/10.1007/978-1-4612-2856-1_98

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97719-5

  • Online ISBN: 978-1-4612-2856-1

  • eBook Packages: Springer Book Archive

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