A canonical process for estimation of convex functions: the "invelope" of integrated Brownian motion + t4.
By P. Groeneboom, Geurt Jongbloed, Jon A. Wellner. 2001
87 citations recorded by the source corpus.
Subfields: Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/fe81c23a480ea5d829b68c018d71f785803034e6
How researchers see this paper
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In Management Science and Operations Research
- Timo Kuosmanen
- Andrew L. Johnson
- Mika Kortelainen
- Jon A. Wellner
- Bodhisattva Sen
- Fadoua Balabdaoui
- Timo Sipiläinen
- Antti Saastamoinen
In Statistics and Probability
- Bodhisattva Sen
- Adityanand Guntuboyina
- Mika Kortelainen
- Fadoua Balabdaoui
- Timo Kuosmanen
- Andrew L. Johnson
- Richard J. Samworth
- Jon A. Wellner
Citations in the corpus
- One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient, root-n consistent StoNEZD method (2011, methodology): “Regarding the asymptotic properties, Hanson and Pledger (1976) have formally proven consistency of the original CNLS estimator, and Groeneboom et al. (2001) have established its asymptotic distribution and the rates of convergence.”
- Estimation of a k-monotone density: limit distribution theory and the Spline connection (2005, background): “When k = 2, Groeneboom, Jongbloed and Wellner [18] considered both the MLE and LSE and established that if the true convex and nonincreasing density g0 satisfies g ′′ 0 (x0) > 0 (and g ′′ 0 is continuous in a neighborhood of x0), then ( n2/5(ḡn(x0)− g0(x0)) n1/5(ḡ′n(x0)− g ′(x0)) ) d → ( ( 124g 2 ”
- Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints (2012, methodology): “…be computed in the single-output case by solving the convex nonparametric least squares (CNLS) problem (Hildreth, 1954; Hanson and Pledger, 1976; Groeneboom et al., 2001a,b; Kuosmanen, 2008) subject to monotonicity and concavity constraints that characterize the frontier, and a sign constraint…”
- Nonparametric Shape-Restricted Regression (2017, background): “1689–1692] that along with the process Zloc n , the “invelope” Hloc n converges in such a way that the second and third derivatives of Hloc n at zero converges in distribution to the corresponding quantities of H; also see [61].”