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The Influence Curve and Goodness of Fit

John R. Michael and William R. Schucany
Journal of the American Statistical Association
Vol. 80, No. 391 (Sep., 1985), pp. 678-682
DOI: 10.2307/2288484
Stable URL: http://www.jstor.org/stable/2288484
Page Count: 5
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The Influence Curve and Goodness of Fit
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Abstract

The influence curve introduced by Hampel (1968) is applied to goodness-of-fit statistics. The efficacy curve is then defined to be the square of the influence curve weighted by a constant that arises in the context of approximate Bahadur efficiency. For a number of goodness-of-fit statistics, the ratios of these curves are shown to be equal to asymptotic relative efficiencies in the Pitman sense when testing for point contamination. These efficacy curves graphically portray the sensitivities of certain goodness-of-fit statistics to minor perturbations in the assumed distribution.

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