Estimating a Regression Function

By Sara A. van de Geer. 1990

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Citations in the corpus

Additive models with trend filtering (2017, background): “5 in van de Geer [1990] (see also van de Geer [2000]).”
Convergence of algorithms for reconstructing convex bodies and directional measures (2006, background): “D P. MILANFAR Note that if X i is a normal N(0,σ2) random variable for i =1,2,..., then this condition is satisﬁed when A=τ =2σ. The following result is due to van de Geer [32], Theorem 9.1 (see also [31]). Proposition 4.1. Let a>0 and let X i, i=1,2,..., be uniformly subGaussian independent rand”
√n-consistent parameter estimation for systems of ordinary differential equations : bypassing numerical integration via smoothing (2010, unknown): “Since the differential equations setting is covered by the general theory of nonlinear least squares, theoretical results available for the latter apply also in the differential equations setting and we refer for example, to [25] and [57], or more generally to [43, 44], and [33] for a thorough treat”
On risk bounds in isotonic and other shape restricted regression problems (2013, background): “The behavior of θ̂ (Y ;M), under the loss 2, has been studied in a number of papers including [6, 14, 21, 29, 30, 33, 35].”
ON THE DEGREES OF FREEDOM IN SHAPE-RESTRICTED REGRESSION (2000, background): “The result itself is known; it appears in the unpublished manuscript of Donoho (1990) and a closely related result appears in Van der Geer (1990).”
Sequential Double Robustness in Right-Censored Longitudinal Models (2017, methodology): “Here we focus on estimators derived from empirical risk minimization (ERM; we also use ERM to denote “empirical risk minimizer”) (see, e.g., van de Geer, 1990; Vapnik, 1991; Bartlett and Mendelson, 2006).”
Model selection via testing: an alternative to (penalized) maximum likelihood estimators (2006, background): “is known to behave in an optimal way for parametric estimation under suitable regularity assumptions (see, for instance, Le Cam [41] or the book [60] by van der Vaart) and to have the right rate of convergence in nonparametric situations under specific entropy assumptions ([57–59,13,54] and [64]).”
On matrix estimation under monotonicity constraints (2015, background): “This risk Rvec(θ∗, θ̂ ) has been studied by a number of authors including van de Geer [22,23], Donoho [11], Birgé and Massart [4], Wang [28], Meyer and Woodroofe [16], Zhang [29] and Chatterjee et al.”
Theory of classification : a survey of some recent advances (2005, methodology): “This technique, which goes back to Huber [110], is used, for example, by van de Geer [224–226].”
Optimal rates of statistical seriation (2016, methodology): “The LS estimator defined by θ̂ = argminθ∈Sn ‖θ− y‖ 2 2 can be computed in closed form in O(n) using the Pool-Adjacent-Violators algorithm (PAVA) [6, 8, 59] and its statistical performance has been studied by Zhang [72] (see also [57, 30, 68, 53, 70] for similar bounds using empirical process theory)”
Risk bounds in isotonic regression (2002, methodology): “As a result, we use relatively “light” probabilistic tools, for example, Doob’s inequality for martingales and “good-λ inequality,” instead of entropy-type arguments, as used, for example, in van de Geer (1990).”
Isotonic regression in general dimensions (2017, background): “…case where d = 1, model (1) reduces to the univariate isotonic regression problem that has a long history (e.g. Brunk, 1955; van Eeden, 1958; Barlow et al., 1972; van de Geer, 1990, 1993; Donoho, 1991; Birgé and Massart, 1993; Meyer and Woodroofe, 2000; Durot, 2007, 2008; Yang and Barber, 2017).”
Adapting to unknown sparsity by controlling the false discovery rate (2005, result): “Up to this point, the development is close to that of Donoho and Johnstone (1994a), as well as work of other authors (e.g. Van de Geer (1990)).”
Convergence rates of least squares regression estimators with heavy-tailed errors (2017, background): “ ERRORS 3 Here we will mainly focus on measuring loss or risk in the sense of the prediction loss (b) since it corresponds to the usual choice in the language of Empirical Risk Minimization; see e.g. [8, 9, 10, 37, 38, 49, 71, 75, 77]. Thus we will (usually) measure loss or risk in L 2(P) and hence ”