Research of the mean cook distance and the robust estimate of scale parameter

Abstract

Based on the principle of statistics and the research results by Zhu Jianjun, the paper establishes the mean Cook distance of scale parameter and studies its properties. The paper still presents the robust estimate of scale parameter with minimum mean Cook distance and theoretically shows that scale parameter is not “nuisance parameter” and it determined by the plus weight squared sums of the residuals of observations. A simple numerical example is given.

Keywords

Cook distance / robust estimate / scale parameter

References

[1] ZhuJianjun. The robust estimate with minimum mean squared error. The Australia Surveyor, 1991, 36(2): 111-115

[2] ZhuJianjun. Robustness and robust estimate. Journal of Geodesy, 1996, 20: 586-590

[3] HuberP JRobust stutistic, 1981, New York, Wiley: 1-1

[4] ZhouJiangwen. Classical theory of errors and robust estimation. Acta Geodetia et cartographica sinica, 1989, 18: 115-120

[5] ZhuJianjun. Least squares estimate under the contaminated model. Journal of Central South University of Technology (in Chinese), 1996, 27(3): 273-277

[6] Huber P J. Robust estimate of a location parameter. Ann Math Statist, 1964, 73–101

[7] HampelF RRobust statistic: The approach based on influence functions, 1986, New York, Wiley: 1-20

[8] CookR D. Weisbery. Characterization of an empirical influence function for detecting influential cases in regression. Technometics, 1980, 22(4): 495-508

[9] Quziqiang. Estimation of variance and covariance components. Bulletin Geodesique, 1989, 63: 139-148