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Interactive nonparametric analysis of nonlinear systems

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  • Das, Sonali
  • Racine, Jeffrey S.

Abstract

In this paper we outline an interactive nonparametric methodology designed to facilitate the statistical analysis of nonlinear systems. The approach exploits an ensemble of nonparametric techniques including conditional density function estimation, conditional distribution function estimation, conditional mean estimation (regression) and conditional quantile estimation (quantile regression). By exploiting recent developments in nonparametric methodology and also in open source interactive platforms for data visualization and statistical analysis, we are able to provide an approach that facilitates enhanced understanding of complex empirical phenomenon. We illustrate this approach by exploring the inherent complexity of the Southern Ocean system as a carbon sink, measured in terms of fugacity of carbon dioxide at sea surface temperature (f CO2), in relation to a number of oceanic state variables, all measured in situ during the annual South African National Antarctic Expedition (SANAE) austral summer trips from Cape Town to the Antarctic, and back, between 2010 and 2015.

Suggested Citation

  • Das, Sonali & Racine, Jeffrey S., 2018. "Interactive nonparametric analysis of nonlinear systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 290-301.
    • Handle: RePEc:eee:phsmap:v:510:y:2018:i:c:p:290-301
    DOI: 10.1016/j.physa.2018.06.071
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    References listed on IDEAS

    as
    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, November.
    2. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    3. Henderson,Daniel J. & Parmeter,Christopher F., 2015. "Applied Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521279680, November.
    4. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    5. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    6. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    7. Li, Qi & Racine, Jeffrey S., 2010. "Smooth Varying-Coefficient Estimation And Inference For Qualitative And Quantitative Data," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1607-1637, December.
    8. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    9. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
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