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Minimax Confidence Intervals for Pointwise Nonparametric Regression Estimation
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2009 (English)In: Proceedings of the 15th IFAC Symposium on System Identification, 2009Conference paper, Published paper (Refereed)
Abstract [en]

We address a problem of estimation of an unknown regression function f at a given point x_0 from noisy observations y_i = f(x_i)+ e_i, ;i =1, ..., n. Here x_i in {cal R}^k 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 F_n = {f(x_i),fin F,i =0, ..., n, } is a convex compact set. For an arbitrary fixed regression plan X_n =(x_1;...;x_n) we study minimax on F_n 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
2009.
Keyword [en]
Non-parametric regression, Linear estimation, Non-parametric identification, Convex programming, Identification algorithms
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-89072OAI: oai:DiVA.org:liu-89072DiVA: diva2:606618
Conference
15th IFAC Symposium on System Identification, Saint Malo, France, July, 2009
Available from: 2013-02-19 Created: 2013-02-19 Last updated: 2013-09-15

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Ljung, Lennart

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