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Model-free model-fitting and predictive distributions

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  • Dimitris Politis

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Abstract

The problem of prediction is revisited with a view towards going beyond the typical nonparametric setting and reaching a fully model-free environment for predictive inference, i.e., point predictors and predictive intervals. A basic principle of model-free prediction is laid out based on the notion of transforming a given setup into one that is easier to work with, namely i.i.d. or Gaussian. As an application, the problem of nonparametric regression is addressed in detail; the model-free predictors are worked out, and shown to be applicable under minimal assumptions. Interestingly, model-free prediction in regression is a totally automatic technique that does not necessitate the search for an optimal data transformation before model fitting. The resulting model-free predictive distributions and intervals are compared to their corresponding model-based analogs, and the use of cross-validation is extensively discussed. As an aside, improved prediction intervals in linear regression are also obtained. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Dimitris Politis, 2013. "Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 183-221, June.
  • Handle: RePEc:spr:testjl:v:22:y:2013:i:2:p:183-221
    DOI: 10.1007/s11749-013-0317-7
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    References listed on IDEAS

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    1. Peter Bickel & Bo Li & Alexandre Tsybakov & Sara Geer & Bin Yu & Teófilo Valdés & Carlos Rivero & Jianqing Fan & Aad Vaart, 2006. "Regularization in statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 271-344, September.
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    6. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
    7. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, May.
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    10. Politis, Dimitris N, 2010. "Model-free Model-fitting and Predictive Distributions," University of California at San Diego, Economics Working Paper Series qt67j6s174, Department of Economics, UC San Diego.
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    Citations

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    Cited by:

    1. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Michael Wolf & Dan Wunderli, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 352-376, May.
    2. Pan, Li & Politis, Dimitris N, 2014. "Bootstrap prediction intervals for linear, nonlinear, and nonparametric autoregressions," University of California at San Diego, Economics Working Paper Series qt67h5s74t, Department of Economics, UC San Diego.
    3. Pan, Li & Politis, Dimitris, 2014. "Bootstrap prediction intervals for Markov processes," University of California at San Diego, Economics Working Paper Series qt7555757g, Department of Economics, UC San Diego.
    4. Stefan Sperlich, 2013. "Comments on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 227-233, June.
    5. Pan, Li & Politis, Dimitris N., 2016. "Bootstrap prediction intervals for Markov processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 467-494.

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