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.
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Zhu Jianjun. The robust estimate with minimum mean squared error. The Australia Surveyor, 1991, 36(2):111–115
Zhu Jianjun. Robustness and robust estimate. Journal of Geodesy, 1996, 20: 586–590
Huber P J. Robust stutistic. New York: Wiley, 1981. 1
Zhou Jiangwen. Classical theory of errors and robust estimation. Acta Geodetia et cartographica sinica, 1989, 18:115–120
Zhu Jianjun. Least squares estimate under the contaminated model. Journal of Central South University of Technology (in Chinese), 1996, 27(3):273–277
Huber P J. Robust estimate of a location parameter. Ann Math Statist, 1964, 73–101
Hampel F R. Robust statistic: The approach based on influence functions. New York: Wiley, 1986, 1–20
Cook R D. Weisbery. Characterization of an empirical influence function for detecting influential cases in regression. Technometics, 1980, 22(4):495–508
Qu ziqiang. Estimation of variance and covariance components. Bulletin Geodesique, 1989, 63:139–148
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Project supported by the National Doctorate Program Funds of China
Synopsis of the author Wang Zhizhong, associate professor, born in 1963, majoring in the theory of surveying adjustment.
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Wang, Z. Research of the mean cook distance and the robust estimate of scale parameter. J Cent. South Univ. Technol. 4, 61–64 (1997). https://doi.org/10.1007/s11771-997-0033-0
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DOI: https://doi.org/10.1007/s11771-997-0033-0