Average case \(L_\infty\)-approximation in the presence of Gaussian noise

DOI10.1006/jath.1998.3175zbMath0913.41019OpenAlexW2092016490MaRDI QIDQ1266109

Leszek Plaskota

Publication date: 31 May 1999

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.1998.3175

zbMATH Keywords

Wiener measureGaussian noiseminimal average error\(L_\infty\)-approximation

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Spline approximation (41A15)

Related Items (2)

Optimal designs for weighted approximation and integration of stochastic processes on \([0,\infty)\) ⋮ Information-based nonlinear approximation: an average case setting

Cites Work

• On average complexity of global optimization problems
• Function approximation and integration on the Wiener space with noisy data
• Asymptotic minimax risk for sup-norm loss: Solution via optimal recovery
• Average-case analysis of numerical problems
• Optimal approximation of linear operators based on noisy data on functionals
• Probabilistic and average linear width in \(L_ \infty\)-norm with respect to \(r\)-fold Wiener measure
• Almost optimal differentiation using noisy data
• Worst case complexity of problems with random information noise
• Approximation and optimization on the Wiener space
• An Asymptotically Minimax Regression Estimator in the Uniform Norm up to Exact Constant
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