Model-free Model-fitting and Predictive Distributions

Dimitris N Politis

University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

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 set-up 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: bootstrap; cross-validation; heteroskedasticity; nonparametric estimation; predictive distribution; predictive intervals; regression; smoothing; Social and Behavioral Sciences (search for similar items in EconPapers)
Date: 2010-03-01
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Citations: View citations in EconPapers (3)

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