Curse of dimensionality and related issues in nonparametric functional regression
By Gery Geenens. 2011
98 citations recorded by the source corpus.
Recently, some nonparametric regression ideas have been extended to the case of functional regression. Within that framework, the main concern arises from the infinite dimensional nature of the explanatory objects. Specifically, in the classical multivariate regression context, it is well-known that any nonparametric method is affected by the socalled “curse of dimensionality”, caused by the sparsity of data in highdimensional spaces, resulting in a decrease in fastest achievable rates of convergence of regression function estimators toward their target curve as the dimension of the regressor vector increases. Therefore, it is not surprising to find dramatically bad theoretical properties for the nonparametric functional regression estimators, leading many authors to condemn the methodology. Nevertheless, a closer look at the meaning of the functional data under study and on the conclusions that the statistician would like to draw from it allows to consider the problem from another point-of-view, and to justify the use of slightly modified estimators. In most cases, it can be entirely legitimate to measure the proximity between two elements of the infinite dimensional functional space via a semi-metric, which could prevent those estimators suffering from what we will call the “curse of infinite dimensionality”. AMS 2000 subject classifications: Primary 62G08; secondary 62M40.
Subfields: Computer Vision and Pattern Recognition, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/506ff50f25e835ff35f8d7e004c290d40599187d
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In Computer Vision and Pattern Recognition
In Statistics and Probability
- Nengxiang Ling
- Philippe Vieu
- Heng Lian
- Peter Hall
- Frédéric Ferraty
- M. Febrero–Bande
- H. Muller
- Antonio Cuevas
Citations in the corpus
- Nonparametric modelling for functional data: selected survey and tracks for future (2018, background): “[11], as well as those selected bibliographical discussions byGeenens [12], Cuevas [13], Jacques andPreda [14], Shang [15], Horváth and Rice [16], Müller [17], Goia and Vieu [18], and Nagy [19], highlight the wide scope of recent advances in FDA.”