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An exploratory data analysis in scale-space for interval-valued data

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  • Cheolwoo Park
  • Yongho Jeon
  • Kee-Hoon Kang

Abstract

We propose an exploratory data analysis approach when data are observed as intervals in a nonparametric regression setting. The interval-valued data contain richer information than single-valued data in the sense that they provide both center and range information of the underlying structure. Conventionally, these two attributes have been studied separately as traditional tools can be readily used for single-valued data analysis. We propose a unified data analysis tool that attempts to capture the relationship between response and covariate by simultaneously accounting for variability present in the data. It utilizes a kernel smoothing approach, which is conducted in scale-space so that it considers a wide range of smoothing parameters rather than selecting an optimal value. It also visually summarizes the significance of trends in the data as a color map across multiple locations and scales. We demonstrate its effectiveness as an exploratory data analysis tool for interval-valued data using simulated and real examples.

Suggested Citation

  • Cheolwoo Park & Yongho Jeon & Kee-Hoon Kang, 2016. "An exploratory data analysis in scale-space for interval-valued data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2643-2660, October.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:14:p:2643-2660
    DOI: 10.1080/02664763.2016.1142947
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    References listed on IDEAS

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    5. Park, Cheolwoo & Huh, Jib, 2013. "Statistical inference and visualization in scale-space using local likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 336-348.
    6. Lima Neto, Eufrasio de A. & de Carvalho, Francisco de A.T., 2008. "Centre and Range method for fitting a linear regression model to symbolic interval data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1500-1515, January.
    7. Park, Cheolwoo & Godtliebsen, Fred & Taqqu, Murad & Stoev, Stilian & Marron, J.S., 2007. "Visualization and inference based on wavelet coefficients, SiZer and SiNos," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5994-6012, August.
    8. Lima Neto, Eufrásio de A. & de Carvalho, Francisco de A.T., 2010. "Constrained linear regression models for symbolic interval-valued variables," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 333-347, February.
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    10. Godtliebsen, Fred & Oigard, Tor Arne, 2005. "A visual display device for significant features in complicated signals," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 317-343, February.
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    12. Cheolwoo Park & J. S. Marron & Vitaliana Rondonotti, 2004. "Dependent SiZer: Goodness-of-Fit Tests for Time Series Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(8), pages 999-1017.
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    Cited by:

    1. Cheolwoo Park & Yongho Jeon & Kee-Hoon Kang, 2017. "Discussion," International Statistical Review, International Statistical Institute, vol. 85(1), pages 33-35, April.
    2. Marta García-Bárzana & Ana Belén Ramos-Guajardo & Ana Colubi & Erricos J. Kontoghiorghes, 2020. "Multiple linear regression models for random intervals: a set arithmetic approach," Computational Statistics, Springer, vol. 35(2), pages 755-773, June.
    3. Lasse Holmström & Leena Pasanen, 2017. "Rejoinder," International Statistical Review, International Statistical Institute, vol. 85(1), pages 43-45, April.

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