Invited Paper


, Volume 22, Issue 2, pp 183-221

First online:

Model-free model-fitting and predictive distributions

  • Dimitris N. PolitisAffiliated withDepartment of Mathematics, University of California—San Diego Email author 

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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.


Bootstrap Cross-validation Frequentist prediction Heteroskedasticity Nonparametric estimation Prediction intervals Regression Smoothing Transformations

Mathematics Subject Classification

62G99 62G08 62G09