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SENSITIVITY ANALYSIS OF *M*-ESTIMATES

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JAN ÁMOS VÍSEK

*Department of Stochastic Informatics, Institute of
Information
Theory and Automation,*

Academy of Sciences the Czech Republic,

and

Department of Macroeconomics, Institute of Economic Studies,

Charles University, Czech Republic
(Received March 22, 1994; revised June 26, 1995)

**Abstract.**
Bahadur representation of the difference of
estimators of regression coefficients for the full data set and for
the set from which one observation was deleted is given for the
*M*-estimators which are generated by a continuous *psi*-function.
The representation is invariant with respect to the scale of
residuals and it indicates that the bound of the norm of the
difference is proportional to the gross error sensitivity. Then for
the *psi*-function which corresponds to the median it is shown that
the difference of the estimates for the full data and for data
without one observation, although being bounded in probability, can
be much larger than indicated by the gross error sensitivity.

*Key words and phrases*:
Sensitivity analysis,
influential points in *M*-estimation, scale invariance.

**Source**
( TeX ,
DVI ,
PS )