Model-free model-fitting and predictive distributions

Dimitris Politis ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2013, vol. 22, issue 2, 183-221

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. Copyright Sociedad de Estadística e Investigación Operativa 2013

Keywords: Bootstrap; Cross-validation; Frequentist prediction; Heteroskedasticity; Nonparametric estimation; Prediction intervals; Regression; Smoothing; Transformations; 62G99; 62G08; 62G09 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:22:y:2013:i:2:p:183-221

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DOI: 10.1007/s11749-013-0317-7

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