Model-free model-fitting and predictive distributions

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...

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Bibliographic Details
Published in:Test (Madrid, Spain) Spain), 2013-06, Vol.22 (2), p.183-221
Main Author: Politis, Dimitris N.
Format: Article
Language:English
Subjects:
Datasets
Economics
Estimates
Finance
Fittings
Hypothesis testing
Insurance
Invited Paper
Management
Mathematics and Statistics
Predictions
Random variables
Regression analysis
Statistical Theory and Methods
Statistics
Statistics for Business
Stochastic models
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Summary: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.
ISSN:1133-0686
1863-8260
DOI:10.1007/s11749-013-0317-7