Estimating a Convex Function in Nonparametric Regression
By Melanie Birke, Holger Dette. 2007
67 citations recorded by the source corpus.
Subfields: Global and Planetary Change, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/8573eeb7eff8d6360014f2c9eb04b86e398736dc
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Global and Planetary Change
- David B. Dunson
- Lauren Hannah
- Bodhisattva Sen
- E. Seijo
- Warrren B Powell
- Stanislav Volgushev
- Holger Dette
In Statistics and Probability
- Lauren Hannah
- David B. Dunson
- Bodhisattva Sen
- Stanislav Volgushev
- E. Seijo
- Christopher F. Parmeter
- Warrren B Powell
- I. Chang
Citations in the corpus
- Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function (2010, methodology): “Some alternative methods of estimation that combine shape restrictions with smoothness assumptions have also been proposed for the one-dimensional case; see, for example, Birke and Dette (2006) where a kernel-based estimator is defined and its asymptotic distribution derived.”
- Multivariate convex regression with adaptive partitioning (2011, methodology): “Key words: Nonparametric regression, shape constraint, convex regression, treed linear model, adaptive partitioning”
- Semiconvex Regression for Metamodeling-Based Optimization (2014, methodology): “Methods include the least squares estimator [39, 22, 34, 47, 29, 75, 24, 27], order restricted splines [71, 48, 49, 65], constrained kernel regression [11], and Bernstein polynomials [18].”
- Shape restricted regression with random Bernstein polynomials (2007, methodology): “(4.4) We note that both F<3> and F<4> are examples in Birke and Dette [3].”
- Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints (2012, background): “For example, restricted kernel smoothing has been considered by Mukerjee (1988), Mammen (1991), Hall and Huang (2001), Braun and Hall (2001), Hall and Kang (2005), Birke and Dette (2007), and Carroll, Delaigle, and Hall (2011), among others; restricted spline smoothing has been studied by Wright and”
- Non‐crossing non‐parametric estimates of quantile curves (2008, result): “This extends recent findings of Birke and Dette (2007), who showed that F̃ −1 .p|x/ and Q̂.p|x/ have the same Lq-norm for all q 1.”