Title: Model-free prediction and regression
Authors: Dimitris Politis - University of California, San Diego (USA) [presenting]
Abstract: Prediction has been traditionally approached via a model-based paradigm, i.e., (a) fit a model to the data at hand, and (b) use the fitted model in order to extrapolate/predict future data. Due to both mathematical and computational constraints, 20th century statistical practice focused mostly on parametric models. Fortunately, with the advent of widely accessible powerful computing in the late 1970s, computer-intensive methods such as the bootstrap and cross-validation freed practitioners from the limitations of parametric models, and paved the way towards the `big data' era of the 21st century.Nonetheless, there is a further step one may take, namely going beyond even nonparametric models. The Model-Free Prediction Principle is based on the simple notion of transforming a complex dataset to one that is easier to work with, e.g., i.i.d. or Gaussian. As such, it restores the emphasis on observable quantities, i.e., current and future data, as opposed to unobservable model parameters and estimates thereof. Coupled with resampling, the Model-Free Prediction Principle allows us to go beyond point prediction in order to construct frequentist prediction intervals without resort to restrictive model assumptions. Furthermore, Model-Free Prediction ideas can be used to additionally obtain point estimates and confidence intervals for quantities of interest, leading to an alternative, transformation-based approach to statistical inference.