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Model-Free Prediction and Regression - A Transformation-Based Approach to Inference (Hardcover, 1st ed. 2015)
Loot Price: R3,808
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Model-Free Prediction and Regression - A Transformation-Based Approach to Inference (Hardcover, 1st ed. 2015)
Series: Frontiers in Probability and the Statistical Sciences
Expected to ship within 10 - 15 working days
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The Model-Free Prediction Principle expounded upon in this
monograph 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, and yields
optimal predictors in diverse settings such as regression and time
series. Furthermore, the Model-Free Bootstrap takes us beyond point
prediction in order to construct frequentist prediction intervals
without resort to unrealistic assumptions such as normality.
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 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, i.e., going beyond even nonparametric models;
this is where the Model-Free Prediction Principle is useful.
Interestingly, being able to predict a response variable Y
associated with a regressor variable X taking on any possible value
seems to inadvertently also achieve the main goal of modeling,
i.e., trying to describe how Y depends on X. Hence, as prediction
can be treated as a by-product of model-fitting, key estimation
problems can be addressed as a by-product of being able to perform
prediction. In other words, a practitioner can use Model-Free
Prediction ideas in order to additionally obtain point estimates
and confidence intervals for relevant parameters leading to an
alternative, transformation-based approach to statistical
inference.
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