Comments on: Model-free model-fitting and predictive distributions
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This paper provides a new useful insight about the problem of constructing prediction intervals with the minimum number of assumptions including invoking any particular model on the data. The overall procedure is based on the model-free prediction principle, which relies on the idea of finding an invertible transformation H such that the data (response and explanatory variables) are mapped onto a i.i.d. vector with distribution Fn. Along Sect. 3, with detailed examples mainly devoted to nonparametric estimators, this idea is employed based on a model, i.e. the transformation H that converts the original data Yt and their covariates Xt into i.i.d. residuals and/or i.i.d. predictive residuals has a closed form chosen by the practitioner. Two methods are proposed in this section. The first one, based on fitted residuals, is called model-based (MB) whereas the second one, based on predictive residuals, is called model-free/model-based(MF/MB). In the paper, a resampling algorithm...
KeywordsConditional Distribution Prediction Interval Predictive Distribution Nonparametric Estimator Functional Data Analysis
I would like to thank the editors of TEST for their invitation to comment on such an interesting paper. This research is partly supported by Grant MTM2008-03010.