M-estimation in a Small Business Survey
DOI:
https://doi.org/10.15678/ZNUEK.2016.0949.0101Keywords:
robust regression, M-estimation, business statistics, outliersAbstract
In many business surveys, sample sizes are large enough to compensate for the presence of outliers, which have a relatively small impact on estimates. However, at low levels of aggregation, the impact of outliers might be significant. Therefore, in the case of a population such as the population of enterprises, the classical approach should be accompanied by methods that resist the occurrence of outliers. To deal with this problem, several alternative technique of estimation, less sensitive to outliers, have been proposed in the statistics literature. In this paper we look at one of them – M-estimation, and compare its usefulness in the small businesses survey.
Downloads
References
Alma Ö.G. [2011], Comparison of Robust Regression Methods in Linear Regression, „International Journal of Contemporary Mathematical Sciences”, vol. 6, nr 9, http://dx.doi.org/10.12988/ijcms.
Banaś M., Ligas M. [2014], Empirical Tests of Performance of Some M-estimators, „Geodesy and Cartography”, vol. 63, nr 2, http://dx.doi.org/10.2478/geocart-2014-0015.
Chen C. [2003], Robust Tools in SAS [w:] Developments in Robust Statistics. International Conference on Robust Statistics, red. R. Dutter i in., Springer Science and Business Media, Berlin–Heidelberg, http://dx.doi.org/10.1007/2F978-3-642-57338-5.
Chen C., Yin G. [2002], Computing the Efficiency and Tuning Constants for M-Estimation, Proceedings of the 2002 Joint Statistical Meetings, American Statistical Association, Alexandria.
Cox B.G., Binder A., Chinnappa N.B., Christianson A., Colledge M.J., Kott P.S. [1995], Business Survey Methods, John Wiley and Sons, Hoboken, NJ, http://dx.doi.org/10.1002/9781118150504.fmatter.
Fair R.C. [1974], On the Robust Estimation of Econometric Models, „Annals of Economic and Social Measurement”, vol. 3.
Hampel F.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.A. [2011], Robust Statistics: The Approach Based on Influence Functions, John Wiley and Sons, Hoboken, NJ, http://dx.doi.org/10.1002/9781118186435.fmatter.
Holland P., Welsch R. [1977], Robust Regression Using Iteratively Reweighted Least-Squares, „Communications in Statistics – Theory and Methods”, vol. 6, http://dx.doi.org/10.1080/03610927708827533.
Huber P.J. [1964], Robust Estimation of a Location Parameter, „Annals of Mathematical Statistics”, vol. 35.
Huber P.J. [1981], Robust Statistics, John Wiley and Sons, New York.
Renaud O., Victoria-Feser M. [2010], A Robust Coefficient of Determination for Regression, „Journal of Statistical Planning and Inference”, vol. 140, nr 7, http://dx.doi.org/10.1016/j.jspi.2010.01.008.
Rousseeuw P.J., Leroy A.M. [1987], Robust Regression and Outlier Detection, Wiley-Interscience, New York.
Trzpiot G. [2013], Wybrane statystyki odporne, „Studia Ekonomiczne”, nr 152.
User’s Guide. The Robustreg Procedure [2014], SAS Institute, Cary, NC.
