Asymptotic equivalence theory for nonparametric regression with random design

By Lawrence D. Brown, Tommaso Cai, Mark G. Low, Cun-Hui Zhang. 2002

102 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/41a68a857a2fef6b8131beeee2ddec50708bb4e9

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Citations in the corpus

Asymptotic equivalence of spectral density estimation and gaussian white noise (2009, background): “Brown and Low [4] and Brown, Low and Zhang [5] obtained constructive results for white noise with drift and Gaussian regression with nonrandom and random design.”
Asymptotic equivalence for nonparametric regression (2024, unknown): “A nonparametric regression model with random design, but Gaussian noise was recently treated by Brown, Low and Zhang [5].”
General empirical Bayes wavelet methods and exactly adaptive minimax estimation (2005, methodology): “ Brown, Cai, Low and Zhang (2002) proved that due to the orthonormality of the mappings TN given {ti}, the inverse mappings of TN provide 46 C.-H.”
Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift (2004, methodology): “ Brown, Cai, Low and Zhang (2002) , Lemma 3] and H 2 (˜ gλ, ϕ� ) ≤ 2.”
Advanced Distribution Theory for SiZer (2006, background): “(For some interesting mathematics that makes these connections precise, see Nussbaum 1996; Brown and Low 1996; Brown, Cai, and Low 2002; Grama and Nussbaum 1998, 2002.)”
SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax (2015, background): “An incomplete list of works working with Gaussian designs would include [20, 5, 13, 21, 58, 8, 31].”
Asymptotic statistical equivalence for scalar ergodic diffusions (2006, methodology): “Even in the case of a regression model with known random design the transformation of a degenerate or unbounded design distribution to a uniform distribution would yield a similar condition on the nonparametric class in order to give asymptotic equivalence ( Brown, Cai, Low, and Zhang 2002, p. 690 )”
Information, Divergence and Risk for Binary Experiments (2009, methodology): “gford et al., 2006; Li and Lin, 2006; Beygelzimer et al., 2007; Langford, 2007; Scott and Davenport, 2007),or development of results which although not explicitly called reductions are eectively so (Brown et al., 2002; Brown and Low, 1996; Brown and Zhao, 2003; Chaudhuri and Loh, 2002; Cossock and Z”
Regression in random design and warped wavelets (2004, result): “In a way, this is strongly linked with the results about the equivalences of experiments (see, for instance Brown, Cai, Low and Zhang (2002) [5]).”
Variance estimation in nonparametric regression via the difference sequence method (2007, background): “We wish to thank T. Cai and L. Wang for pointing out the significance of the article of Hall and Carroll [20] and its relation to our (14).”