Influence Functions for the Moment Estimators

Abstract

Influence functions give a measure of robustness of the statistics estimated from a sample against the sample data. In this study, first, the concept of influence functions is  xamined, and then the influence functions for mean and variance are given. The influence functions for skewness and  urtosis are examined for both asymmetrical and symmetrical distributions and the influence function concept is generalized for scaled moments.

 

Key Words: Influence Functions, Skewness Measure, Kurtosis Measure. 

Keywords

• -

References

1. Huber, P.J., “Robust Estimation of a Location Parameter”, Annals of Mathematical Statistics, 35: 73-101 (1964).
2. Huber, P.J., “Robust Statistics”, New York, John Willey (1981).
3. Hampel, F.R., Rousseeuw, P.J., Stahel, W.A., Ronchetti, E.M., “Robust Statistics: The Approach Based on Influence Functions”, New York, John Willey (1986).
4. Hampel, F.R., “The Influence Curve and Its Role in Robust Estimation”, Journal of the American Statistical Association, 69: 383-393 (1974).
5. Stuart, A., Ord, J.K., “Kendall’s Advanced Theory of Statistics”, New York, Oxford University Press, Vol I (1987).
6. Groeneveld, R.A., “An Influence Function Approach to Describing the Skewness of a Distribution”, The American Statistician, 45: 97- 102 (1991).
7. Ruppert, D., “What is Kurtosis? : An Influence Function Approach”, The American Statistician, 41: 1-5 (1987).