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The Model-Free Prediction Principle

  • Chapter
Model-Free Prediction and Regression

Part of the book series: Frontiers in Probability and the Statistical Sciences ((FROPROSTAS))

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. The Model-Free Prediction Principle is defined, and its applicability to different settings is outlined.

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Notes

  1. 1.

    The notation i.i.d. \((\mu,\sigma ^{2})\) is shorthand for i.i.d. with mean μ and variance \(\sigma ^{2}.\)

  2. 2.

    Indeed, Politis (2013) employed definition (2.12) in a regression context; note, however, that when the responses Y 1, Y 2, … are independent, definitions (2.11) and (2.12) coincide since in this case the theoretical predictor \(\varPi (g,g_{n+1},\underline{Y }_{n},\mathbf{X}_{n+1},F_{n+1})\) does not depend on its third argument, namely \(\underline{Y }_{n}\), at all.

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    Dimitris N. Politis

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Politis, D.N. (2015). The Model-Free Prediction Principle. In: Model-Free Prediction and Regression. Frontiers in Probability and the Statistical Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-21347-7_2

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