- Title
- Estimation of a regression function by maxima of minima of linear functions
- Creator
- Bagirov, Adil; Clausen, Conny; Kohler, Michael
- Date
- 2009
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/31920
- Identifier
- vital:1770
- Identifier
-
https://doi.org/10.1109/TIT.2008.2009835
- Identifier
- ISSN:0018-9448
- Abstract
- In this paper, estimation of a regression function from independent and identically distributed random variables is considered. Estimates are defined by minimization of the empirical L2 risk over a class of functions, which are defined as maxima of minima of linear functions. Results concerning the rate of convergence of the estimates are derived. In particular, it is shown that for smooth regression functions satisfying the assumption of single index models, the estimate is able to achieve (up to some logarithmic factor) the corresponding optimal one-dimensional rate of convergence. Hence, under these assumptions, the estimate is able to circumvent the so-called curse of dimensionality. The small sample behavior of the estimates is illustrated by applying them to simulated data. © 2009 IEEE.
- Publisher
- IEEE
- Relation
- IEEE Transactions on Information Theory Vol. 55, no. 2 (2009), p. 833-845
- Rights
- Copyright IEEE
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- Adaptation; Dimension reduction; L2 error; Nonparametric regression; Rate of convergence; Single index model; Random variables; Regression analysis; L error; Risk perception
- Full Text
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