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Sharpening Wald-type inference in robust regression for small samples

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  • Koller, Manuel
  • Stahel, Werner A.

Abstract

The datasets used in statistical analyses are often small in the sense that the number of observations n is less than 5 times the number of parameters p to be estimated. In contrast, methods of robust regression are usually optimized in terms of asymptotics with an emphasis on efficiency and maximal bias of estimated coefficients. Inference, i.e., determination of confidence and prediction intervals, is proposed as complementary criteria. An analysis of MM-estimators leads to the development of a new scale estimate, the Design Adaptive Scale Estimate, and to an extension of the MM-estimate, the SMDM-estimate, as well as a suitable [psi]-function. A simulation study shows and a real data example illustrates that the SMDM-estimate has better performance for small n/p and that the use the new scale estimate and of a slowly redescending [psi]-function is crucial for adequate inference.

Suggested Citation

  • Koller, Manuel & Stahel, Werner A., 2011. "Sharpening Wald-type inference in robust regression for small samples," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2504-2515, August.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:8:p:2504-2515
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    2. Krüger, Jens J. & Rhiel, Mathias, 2016. "Determinants of ICT infrastructure: A cross-country statistical analysis," Darmstadt Discussion Papers in Economics 228, Darmstadt University of Technology, Department of Law and Economics.
    3. Viktoria Öllerer & Andreas Alfons & Christophe Croux, 2016. "The shooting S-estimator for robust regression," Computational Statistics, Springer, vol. 31(3), pages 829-844, September.
    4. Clemens B. Fell & Cornelius J. König, 2016. "Is there a gender difference in scientific collaboration? A scientometric examination of co-authorships among industrial–organizational psychologists," Scientometrics, Springer;Akadémiai Kiadó, vol. 108(1), pages 113-141, July.
    5. Oliver Hümbelin, 2016. "Nichtbezug von Sozialhilfe: Regionale Unterschiede und die Bedeutung von sozialen Normen," University of Bern Social Sciences Working Papers 21, University of Bern, Department of Social Sciences, revised 26 Oct 2016.
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    7. Jens J. Krüger, 2017. "Revisiting the world technology frontier: a directional distance function approach," Journal of Economic Growth, Springer, vol. 22(1), pages 67-95, March.
    8. Conradt, Sarah & Bokusheva, Raushan & Finger, Robert & Kussaiynov, Talgat, 0. "Yield Trend Estimation in the Presence of Farm Heterogeneity and Non-linear Technological Change," Quarterly Journal of International Agriculture, Humboldt-Universität zu Berlin, vol. 53.
    9. Mikołaj Szołtysek & Radoslaw Poniat & Siegfried Gruber & Sebastian Klüsener, 2016. "The Patriarchy Index: a new measure of gender and generational inequalities in the past," MPIDR Working Papers WP-2016-014, Max Planck Institute for Demographic Research, Rostock, Germany.
    10. Li, J. & Nott, D.J. & Fan, Y. & Sisson, S.A., 2017. "Extending approximate Bayesian computation methods to high dimensions via a Gaussian copula model," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 77-89.
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    13. Morgan, Peter & Regis, Paulo José & Salike, Nimesh, 2015. "LTV policy as a macroprudential tool: The case of residential mortgage loans in Asia," RIEI Working Papers 2015-03, Xi'an Jiaotong-Liverpool University, Research Institute for Economic Integration.
    14. Soukissian, Takvor H. & Karathanasi, Flora E., 2016. "On the use of robust regression methods in wind speed assessment," Renewable Energy, Elsevier, vol. 99(C), pages 1287-1298.
    15. Martin, Ryan & Han, Zhen, 2016. "A semiparametric scale-mixture regression model and predictive recursion maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 75-85.

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