Additive Regression and Other Nonparametric Models

By C. Stone. 1985

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Citations in the corpus

Additive models with trend filtering (2017, background): “Applying Theorem 3 of Tibshirani & Taylor (2012), we see that df(T θ̂) = E [ dim ( Tnull(D−A) )] , where A = supp(Dθ̂), and where D−A denotes the matrix D with rows removed that correspond to the set A.”
Consistency of Random Forests (2014, methodology): “Additive regression models, which extend linear models, were popularized by Stone (1985) and Hastie and Tibshirani (1986).”
Bivariate Penalized Splines for Regression (2013, methodology): “Under some conditions (von Golitchek and Schumaker (2002a) and Huang (2003b)), P0 is a bounded operator on S in the maximum norm.”
Projection estimation in multiple regression with application to functional ANOVA models (1998, methodology): “In particular, rates of convergence for estimation of additive m o d e l s were established in Stone 1985 for regression and in Stone 1986 for generalized regression.”
Semiparametric Regression Pursuit (2012, background): “Under condition (A3), by Lemma 1 of Stone (1985) and Proposition 2 in Appendix 4 of Bickel, Ritov, Klaassen and Wellner (1993), the sumspace H is closed.”
Penalized Estimation in Additive Regression with High-Dimensional Data (2017, background): “In a classical setting (e.g., Stone 1985), each g∗j is a univariate function and x (j) is the jth component of x ∈ [0, 1]d, so that p = d.”
Oracally Efficient Two-Step Estimation of Generalized Additive Model (2013, unknown): “Articles on additive models and related works include, among others, Stone (1985), Stone (1994), Huang and Yang (2004), and Xue and Yang (2006a) for B-spline methods; Tjøstheim and Auestad (1994), Linton and Nielsen (1995), Linton (1997), Fan, Härdle, and Mammen (1998), Yang, Härdle, and Nielsen…”
Doubly penalized estimation in additive regression with high-dimensional data (2019, background): “In a classical setting (e.g., Stone (1985)), each g∗j is a univariate function and x(j) is the j th component of x ∈ [0,1]d , so that p = d .”