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Local conditional influence. (English) Zbl 1516.62550

Summary: Through an investigation of normal curvature functions for influence graphs of a family of perturbed models, we develop the concept of local conditional influence. This concept can be used to study masking and boosting effects in local influence. We identify the situation under which the influence graph of the unperturbed model contains all the information on these effects. The linear regression model is used for illustration and it is shown that the concept developed is consistent with A. J. Lawrance’s [J. R. Stat. Soc., Ser. B 57, No. 1, 181–189 (1995; Zbl 0825.62578)] approach of conditional influence in Cook’s distance.

MSC:

62-XX Statistics

Citations:

Zbl 0825.62578
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References:

[1] Atkinson, A. C. 1986. In discussion of ‘Influential observations, high leverage points, and outliers in linear regression’ by S. Chatterjee & A.S. Hadi. Statistical Science, 1: 379-416. · Zbl 0633.62059 · doi:10.1214/ss/1177013624
[2] Cook, R. D. 1986. Assessment of local influence (with discussion). Journal of Royal Statistical Society, B, 2: 133-169. · Zbl 0608.62041
[3] Lawrance, A. J. 1991. “Local and deletion influence”. In Directions in Robust Statistics and Diagnostics, Edited by: Stahel, W. and Weisberg, S. Vol. part 1, 141-157. Berlin: Springer.
[4] Lawrance, A. J. 1995. Deletion influence and masking in regression. Journal of Royal Statistical Society, B, 57: 181-189. · Zbl 0825.62578
[5] Pena, D. and Yohai, V. J. 1995. The detection of influential subsets in linear regression by using an influence matrix. Journal of Royal Statistical Society, B, 57: 145-156. · Zbl 0825.62579
[6] Poon, W. Y. and Poon, Y. S. 1999. Conformal normal curvature and assessment of local influence. Journal of Royal Statistical Society, B, 61: 51-61. · Zbl 0913.62062 · doi:10.1111/1467-9868.00162
[7] Poon, W. Y. and Poon, Y. S. 2001. Conditional local influence in case-weights linear regression. British Journal of Mathematical and Statistical Psychology, 54: 177-191.
[8] Thorpe, J. A. 1979. Elementary Topics in Differential Geometry, New York: Springer. · Zbl 0404.53001 · doi:10.1007/978-1-4612-6153-7
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