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The measure of mean cook distance under the contaminated error model

  • Mining, Materials And Information Engineering
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Abstract

Redefines the mean Cook distance under the contaminated error model. With the help of the mean Cook distance, the paper discusses the relationship between local influence of small perturbations and high leverage case. A new robust method for the adjustment of geodetic networks is proposed. The suggested method, a generalization of the robust method with the minimum mean Cook distance, is more efficient than the others. The basic feature of the method is that the equivalent weight functions of the robust estimates are determined according to the principle of statistics.

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References

  1. Hampel F R. Robust statistic: The approach based on influence functions. New York: Wiley, 1986. 1–20

    MATH  Google Scholar 

  2. Huber P J. Robust statistic. New York: Wiley, 1981

    Google Scholar 

  3. Huber P J. Robust estimate of a location parameter. Ann Math Statist, 1964, 35: 73–101

    MathSciNet  Google Scholar 

  4. Zhu Jianjun. The robust estimate with minimum mean squared error. The Australia Surveyor, 1991, 36(2): 111–115

    Google Scholar 

  5. Zhu Jianjun. Robustness and robust estimate. Journal of Geodesy, 1996, 20: 586–590

    Article  Google Scholar 

  6. Zhou Jiangwen. Classical theory of errors and robust estimation. Acta Geodetia et Cartographica Sinica, 1989, 18: 115–120

    Google Scholar 

  7. Koch K R. Maximum likelihood estimation of variance components. Bull Geod, 1986, 60: 329–338

    Article  Google Scholar 

  8. Ou Ziqiang. Estimation of variance and covariance components. Bull Geod, 1989, 63: 139–148

    Article  Google Scholar 

  9. Zhu Jianjun. Least squares estimate under the contaminated model. Journal of Central South University of Technology (in Chinese), 1996, 27(3): 273–277

    Google Scholar 

  10. Wang Zhizhong. Universal formulae of robust estimates of parameter vector and variance component. Transactions of nonferrous metals society of China, 1997, 7(4): 160–163

    Google Scholar 

  11. Wang Zhizhong. Research of the mean Cook distance and the robust estimate of scale parameter. Journal of Central South University of Technology (English Edition), 1997, 4(1): 61–64

    Article  Google Scholar 

  12. Yang Yuanxi. Robust estimation for dependent observations. Manuscripta Geodaetica, 1994, 19: 10–17

    Google Scholar 

Download references

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Authors and Affiliations

  1. College of Resources, Environment and Civil Engineering, Central South University of Technology, 410083, Changsha, China

    Wang Zhizhong & Zhu Jianjun

Authors
  1. Wang Zhizhong
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  2. Zhu Jianjun
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Project supported by the National Natural Science Foundation of China

Synopsis of the first author Wang Zhizhong, associate professor, born in 1963, majoring in the theory of surveying adjustment.

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Wang, Z., Zhu, J. The measure of mean cook distance under the contaminated error model. J Cent. South Univ. Technol. 6, 115–119 (1999). https://doi.org/10.1007/s11771-999-0011-9

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  • DOI: https://doi.org/10.1007/s11771-999-0011-9

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