Projection-based approximation and a duality with kernel methods

DOI10.1214/aos/1176347004zbMath0699.62067OpenAlexW2058802470MaRDI QIDQ913418

David L. Donoho, Iain M. Johnstone

Publication date: 1989

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176347004

zbMATH Keywords

convergencenoisy dataapproximationkernel regressionHermite polynomialssmoothnessLaplacianharmonic functionscurse of dimensionalitydimensionality reductionGaussian measureradial functionslocal averagingtwo-dimensional problemangular smoothnessL2-approximation errorminimax rate ofProjection pursuit regressionrates of

Mathematics Subject Classification ID

Multivariate analysis (62H99) General nonlinear regression (62J02) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Nonparametric inference (62G99)

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