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Robust projection indices

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  • Guy P. Nason

Abstract

Loosely speaking a robust projection index is one that prefers projections involving true clusters over projections consisting of a cluster and an outlier. We introduce a mathematical definition of one‐dimensional index robustness and describe a numerical experiment to measure it. We design five new indices based on measuring divergence from Student's t‐distribution which are intended to be especially robust: the experiment shows that they are more robust than several established indices. The experiment also reveals more generally that the robustness of moment indices depends on the number of approximation terms, providing additional practical guidance for existing projection pursuit implementations. We investigate the theoretical properties of one new Student t‐index and Hall's index and show that the new index automatically adapts its robustness to the degree of outlier contamination. We conclude by outlining the possibilities for extending our experiments to both higher dimensions and other new indices.

Suggested Citation

  • Guy P. Nason, 2001. "Robust projection indices," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 551-567.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:3:p:551-567
    DOI: 10.1111/1467-9868.00298
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    Cited by:

    1. Nason, Guy P., 2006. "On the sum of t and Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1280-1286, July.
    2. Yi Ge & Guangfei Yang & Yi Chen & Wen Dou, 2019. "Examining Social Vulnerability and Inequality: A Joint Analysis through a Connectivity Lens in the Urban Agglomerations of China," Sustainability, MDPI, vol. 11(4), pages 1-19, February.
    3. Yi Ge & Wen Dou & Xiaotao Wang & Yi Chen & Ziyuan Zhang, 2021. "Identifying urban–rural differences in social vulnerability to natural hazards: a case study of China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(3), pages 2629-2651, September.
    4. Yi Ge & Haibo Zhang & Wen Dou & Wenfang Chen & Ning Liu & Yuan Wang & Yulin Shi & Wenxin Rao, 2017. "Mapping Social Vulnerability to Air Pollution: A Case Study of the Yangtze River Delta Region, China," Sustainability, MDPI, vol. 9(1), pages 1-15, January.
    5. Loperfido, Nicola, 2018. "Skewness-based projection pursuit: A computational approach," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 42-57.
    6. Cardinali Alessandro & Nason Guy P, 2011. "Costationarity of Locally Stationary Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-35, January.

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