ON THE DEGREES OF FREEDOM IN SHAPE-RESTRICTED REGRESSION

By Mary C. Meyer, Michael Woodroofe. 2000

161 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/61f53054eecddcca3f78915e70c62aa80af1ec8f

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Citations in the corpus

INFERENCE USING SHAPE-RESTRICTED REGRESSION SPLINES (2008, methodology): “The golden section search method [see Press et al. (1992), Section 10.”
Penalized triograms: total variation regularization for bivariate smoothing (2004, methodology): “The recent work of Meyer and Woodroofe (2000) gives additional support for this choice-they considered the divergence”
PENALIZED LINEAR UNBIASED SELECTION (2007, background): “We refer to Efron (1986) and Meyer and Woodroofe (2000) for more discussions about (4.10) and (4.11).”
On risk bounds in isotonic and other shape restricted regression problems (2013, methodology): “It was also shown in [21] that D(Y ;K) is the number of distinct values among θ̂1, .”
Risk bounds in isotonic regression (2002, background): “Recently, Meyer and Woodroofe (2000) obtained bounds for R2n,2(f ) for i.i.d. normal errors based on Stein’s (1981) unbiased estimation of mean squared errors.”
Isotonic regression in general dimensions (2017, background): “In the special 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 Bar”
On matrix estimation under monotonicity constraints (2015, background): “Because TM(θ) is a closed convex cone, the projection (ε, TM(θ)) satisfies (see, for example, [16], equation (4)): 〈 ε − (ε, TM(θ)), (ε, TM(θ))〉 = 0.”
Nearly unbiased variable selection under minimax concave penalty (2010, background): “We refer to Efron (1986) and Meyer and Woodroofe (2000) for more discussions about (5.8) and (5.9).”
Akaike's Information Criterion, Cp and Estimators of Loss for Elliptically Symmetric Distributions (2014, methodology): “Mallows’s idea was to propose an unbiased estimator of the scaled expected prediction error Eˇ X ǑI Xˇ 2 = 2 , where ǑI is an estimator of ˇ based on the selected variables set I ¹1; : : : ; pº, Eˇ denotes the expectation with respect to the sampling distribution in model (1) and k k is the Euclid”
Penalized Quantile Regression for Dynamic Panel Data (2010, background): “As Meyer and Woodroofe (2000) and Li and Zhu (2008) observe, it turns out that in the case of l1-norm QR case, the number of interpolated data points is a convenient estimate for the effective dimension of the model.”
Shape constrained additive models (2015, methodology): “The edf can be found, following Meyer and Woodroofe (2000) as τ = n∑ i=1 ∂μ̂i ∂yi = tr(KKTL+), (3) where L+ is the diagonal matrix such that L+i i = { α(μi ) −1, if wi ≥ 0 −α(μi )−1, otherwise.”
Quantile Regression in Reproducing Kernel Hilbert Spaces (2007, background): “Since then, many authors have argued that ∑n i=1 ∂ f̂ (xi)/∂yi can be considered an estimate of the effective dimension for a general modeling procedure (e.g., Efron 1986; Ye 1998; Meyer and Woodroofe 2000; Koenker 2005).”
Additive models for quantile regression: Model selection and confidence bandaids (2010, result): “This definition of p(λ) can be viewed from a more unified perspective as consistent with the definition proposed by Meyer and Woodroofe (2000), p(λ) = div(ĝ) = n∑ i=1 ∂ĝ(xi, zi) ∂yi ; see Koenker (2005, p. 243).”
L1-Norm Quantile Regression (2008, background): “Meyer and Woodroofe (2000) discussed (3.1) in shape-restricted regression and also argued that it provides a measure of the effective dimension.”
Sharp oracle inequalities for Least Squares estimators in shape restricted regression (2015, background): “, μn) T ∈ S↑ n, it is known [13, 19, 7, 8] that for some absolute constant c > 0,”