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• W1972805551 abstract "We consider the problem of estimating an unknown function f in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis { ψ jk (G),j,k} warped with the design. This allows us to employ a very stable and computable thresholding algorithm. We investigate the properties of this new basis. In particular, we prove that if the design has a property of Muckenhoupt type, this new basis behaves quite similarly to a regular wavelet basis. This enables us to prove that the associated thresholding procedure achieves rates of convergence which have been proved to be minimax in the uniform design case." @default.
• W1972805551 created "2016-06-24" @default.
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• W1972805551 date "2004-12-01" @default.
• W1972805551 modified "2023-10-16" @default.
• W1972805551 title "Regression in random design and warped wavelets" @default.
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• W1972805551 doi "https://doi.org/10.3150/bj/1106314850" @default.
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