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. 1997 Jan 1;26(3):10.1080/03610927708831932.
doi: 10.1080/03610927708831932.

THE DISTRIBUTION OF COOK'S D STATISTIC

Keith E Muller  1 , Mario Chen Mok  1
Affiliations

THE DISTRIBUTION OF COOK'S D STATISTIC

Keith E Muller et al. Commun Stat Theory Methods. .

Abstract

Cook (1977) proposed a diagnostic to quantify the impact of deleting an observation on the estimated regression coefficients of a General Linear Univariate Model (GLUM). Simulations of models with Gaussian response and predictors demonstrate that his suggestion of comparing the diagnostic to the median of the F for overall regression captures an erratically varying proportion of the values. We describe the exact distribution of Cook's statistic for a GLUM with Gaussian predictors and response. We also present computational forms, simple approximations, and asymptotic results. A simulation supports the accuracy of the results. The methods allow accurate evaluation of a single value or the maximum value from a regression analysis. The approximations work well for a single value, but less well for the maximum. In contrast, the cut-point suggested by Cook provides widely varying tail probabilities. As with all diagnostics, the data analyst must use scientific judgment in deciding how to treat highlighted observations.

Keywords: influence; regression diagnostics; residual analysis.

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References

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    1. Chen Mok M. Evaluating Cook’s D Statistic in Theory and Practice: A Simulation Study. Department of Biostatistics, University of North Carolina; Chapel Hill: 1993. Unpublished Master’s Paper.
    1. Cook RD. Detection of Influential Observations in Linear Regression. Technometrics. 1977;19:15–18.

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