Robust regression in monthly business survey

Grażyna Dehnel

doi:https://doi.org/10.59170/stattrans-2015-008

Robust regression in monthly business survey

Grażyna Dehnel Poznan University of Economics, Department of Statistics Statistics in Transition new series, vol. 16, 2015, 1, pages: 137-152 Published online: 2 March 2015 https://doi.org/10.59170/stattrans-2015-008

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ARTICLE

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ABSTRACT

There are many sample surveys of populations that contain outliers (extreme values). This is especially true in business, agricultural, household and medicine surveys. Outliers can have a large distorting influence on classical statistical methods that are optimal under the assumption of normality or linearity. As a result, the presence of extreme observations may adversely affect estimation, especially when it is carried out at a low level of aggregation. To deal with this problem, several alternative techniques of estimation, less sensitive to outliers, have been proposed in the statistical literature. In this paper we attempt to apply and assess some robust regression methods (LTS, M-estimation, S-estimation, MM-estimation) in the business survey conducted within the framework of official statistics.

KEYWORDS

robust regression, outlier detection, business statistics.

REFERENCES

ALMA, Ö., G., (2011). Comparison of Robust Regression Methods in Linear Regression, [in:] Int. J. Contemp. Math. Sciences, Vol. 6, no. 9, pp. 409-421.

CHEN, C., (2007). Robust Regression and Outlier Detection with the ROBUSTREG Procedure, SUGI, http://www2.sas.com/proceedings/sugi27/pp.265-27.pdf.

COX, B. G., BINDER, A., CHINNAPPA, N. B., CHRISTIANSON, A., COLLEDGE, M. J., KOTT, P. S., (1995). Business Survey Methods, John Wiley and Sons.

GROSS, W. F., BODE, G., TAYLOR, J. M., LLOYD–SMITH, C. W., (1986). Some finite population estimators which reduce the contribution of outliers, [in:] Proceedings of the Pacific Statistical Conference, 20-24 May 1985,Auckland, New Zealand.

HUBER, P. H., (1964). Robust estimation of a location parameter, The Annals of Mathematical Statistics, 35, pp.7-101.

HUBER, P. H., (1981). Robust Statistics, New York: John Wiley and Sons.

ROUSSEEUW, P. J., (1984). Least Median of Squares Regression, [in:] Journal of the American Statistical Association, 79, pp. 871-880.

ROUSSEEUW, P. J., YOHAI, V., (1984). Robust regression by means of S estimators, [in:] W. H. J. Franke and D. Martin (Editors.), Robust and Nonlinear Time Series Analysis, Springer-Verlag, New-York, pp. 256-272.

ROUSSEEUW, P. J., LEROY, A. M., (1987). Robust Regression and Outlier Detection. Wiley-Interscience, New York.

ROUSSEEUW, P. J., DRIESSEN, K., (1998). Computing LTS regression for large data sets, Technical Report, University of Antwerp.

STROMBERG, A. J., (1993). Computation of high breakdown nonlinear regression parameters, [in:] Journal of the American Statistical Association, 88 (421).

VERARDI, V., CROUX, C., (2009). Robust regression in Stata, [in:] The Stata Journal, 9, Number 3, pp. 439-453.

YOHAI,V.J., (1987). High breakdown-point and high efficiency robust estimates for regression, The Annals of Statistics, 15, pp. 642-656