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CPS2204 T. von R. et al.

The ̂ is a diagnostic measure for assessing the simultaneous
,
̂
influence of several observations on the parameter estimates, . Since all
parameters in the model are estimated from the perturbed model, ̂ is
,
regarded to be a joint-parameter influence measure. It can be of interest to
assess the influence of multiple observations on a particular parameter
̂
estimate, , in model (1). If this is the case, we use the same methodology as

above and obtain a marginal-parameter influence measure.

̂
̂
̂
Let = ( , )be a vector of parameter estimates, where

1
̂
̂
̂
= ( , . . . , ̂ −1 , ̂ +1 , … , ),
1

1

are the maximum likelihood estimates from the unperturbed model (1), and
̂
is estimated from the perturbed model (11).

References
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133{169.
2. D.A. Belsley, E. Kuh, and R.E. Welsch, (1980), Regression Diagnostics:
Identifying Inuential Data and Sources of Collinearity, New York: John
Wiley.
3. N. Billor and R.M. Loynes Local inuence: A new approach, Comm. Statist-
Theory Meth. 22 (1993), pp. 1595{1611.
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linear regression, J. Amer. Statist. Assoc. 74 (1979), pp. 169{174.
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6. B. Efron and R.J. Tibshirani (1993). An Introduction to Bootstrap. New
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Simonoff Procedures for the identi_cation of multiple outliers in linear
models, Jour. Amer. Statist. Assoc 88 (1993), pp. 1264{1272.
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Jour. Amer. Statist. Assoc. 83 (1990), pp. 1067{1072.
9. P. Prescott An approximation test for outliers in linear models,
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10. S. Weisberg (1985). Applied Linear Regression. 2nd. Ed. New York: Wiley

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