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Minimax Confidence Intervals for Pointwise Nonparametric Regression Estimation
LJK, BP 53, F-38041 Grenoble Cedex 9, France.
Institute of Control Sciences, Russian Acad. Sci., Moscow, Russia.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
School of ISyE, Georgia Institute of Technology Atlanta, USA.
2009 (English)Report (Other academic)
Abstract [en]

We address a problem of estimation of an unknown regression function f at a given point x0 from noisy observations yi = f(xi)+ ei, ;i =1, ..., n. Here xi in ε Rk are observable regressors and (e_i) are normal i.i.d. (unobservable) disturbances. The problem is analyzed in the minimax framework, namely, we suppose that f belongs to some functional class F, such that its finite-dimensional cut Fn = {f(xi), f ε F, i =0, ..., n, } is a convex compact set. For an arbitrary fixed regression plan Xn =(x1;...;xn) we study minimax on Fn confidence intervals of affine estimators and construct an estimator which attains the minimax performance on the class of arbitrary estimators when the confidence level approaches 1.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2009. , 8 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2908
Keyword [en]
Non-parametric regression, Linear estimation, Non-parametric identification, Convex programming, Identification algorithms
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-56069ISRN: LiTH-ISY-R-2908OAI: diva2:316869
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-08-12Bibliographically approved

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ReferencesLink to record
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