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Scaling01:26

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In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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PERTURBATION AND SCALED COOK'S DISTANCE.

Hongtu Zhu1, Joseph G Ibrahim, Hyunsoon Cho

  • 1Department of Biostatistics, University of North Carolina at Chapel Hill.

Annals of Statistics
|November 16, 2012
PubMed
Summary

This study introduces scaled Cook's distances for complex data, addressing how subset deletion affects model influence. New methods enable robust comparison of influential subsets in advanced statistical modeling.

Area of Science:

  • Statistics
  • Statistical Modeling
  • Data Analysis

Background:

  • Cook's distance is vital for identifying influential observations in linear regression.
  • Existing methods struggle with complex data structures like longitudinal data.
  • Subset deletion with varying sizes causes unequal model perturbation, complicating influence analysis.

Purpose of the Study:

  • To develop a rigorous approach for influence analysis in general parametric models with complex data structures.
  • To address the issue of comparing Cook's distances when deleting subsets of different sizes.
  • To propose a new quantity for measuring the perturbation caused by subset deletion.

Main Methods:

  • Proposing a novel quantity to measure the degree of perturbation from subset deletion.

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  • Utilizing stochastic ordering to quantify the relationship between perturbation degree and Cook's distance magnitude.
  • Developing several scaled Cook's distances for comparing influence across different subset deletions.

    • Main Results:

    • A new framework for influence analysis in complex data structures is established.
    • Scaled Cook's distances effectively resolve comparisons of Cook's distance for varying subset deletions.
    • Theoretical and numerical examples demonstrate the broad applicability of the proposed methods.

    Conclusions:

    • The developed scaled Cook's distances offer a robust solution for influence analysis in complex parametric models.
    • This work extends the utility of Cook's distance beyond simple linear regression and cross-sectional data.
    • The proposed methods facilitate more accurate identification and comparison of influential subsets in advanced statistical applications.