TEST

, Volume 22, Issue 2, pp 183–221

Model-free model-fitting and predictive distributions

Invited Paper

DOI: 10.1007/s11749-013-0317-7

Cite this article as:
Politis, D.N. TEST (2013) 22: 183. doi:10.1007/s11749-013-0317-7

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.

Keywords

BootstrapCross-validationFrequentist predictionHeteroskedasticityNonparametric estimationPrediction intervalsRegressionSmoothingTransformations

Mathematics Subject Classification

62G9962G0862G09

Copyright information

© Sociedad de Estadística e Investigación Operativa 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California—San DiegoLa JollaUSA