Point Estimates of Ordinates of Concave Functions

By C. Hildreth. 1954

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Citations in the corpus

QUASI-CONCAVE DENSITY ESTIMATION (2010, background): “Concavity constraints have played a significant role in non-parametric regression since the seminal work of Hildreth (1954) , but shape restricted estimation of densities has has received little attention until very recently.”
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): “The equivalence result established by Kuosmanen and Johnson (2010) provides the means to integrate the two optimization problems using convex nonparametric least squares (CNLS: Hildreth 1954; Hanson and Pledger 1976; Groeneboom et al. 2001).”
A variable selection approach to monotonic regression with Bernstein polynomials (2011, methodology): “Studies on shape-restricted regression begin with Hildreth 30 who proposes a method for estimating points along a concave function and Brunk 4 who presents maximum likelihood estimators for estimating monotone restrictions on parameters.”
Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints (2012, methodology): “…classic output-oriented DEA estimator can 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…”
Multivariate convex regression with adaptive partitioning (2011, methodology): “Despite being introduced by Hildreth (1954), it has not been implemented in many practical settings (Lim 2010) and has only very recently been shown to be consistent (Seijo & Sen 2011, Lim & Glynn 2011).”
Semiconvex Regression for Metamodeling-Based Optimization (2014, methodology): “Regression subject to convexity constraints, called “convex regression,” has been studied since the 1950’s [39].”
Estimating a Convex Function in Nonparametric Regression (2007, background): “In the case of concave (convex) regression, a concave (convex) least squares estimate was first proposed by Hildreth (1954) and its consistency was proved by Hanson & Pledger (1976).”
Restrictions of economic theory in nonparametric methods (1994, methodology): “The algorithms by Dykstra and by Goldman and Ruud are extensions of the method proposed by Hildreth (1954).”
Nonparametric Shape-Restricted Regression (2017, methodology): “Shape-constrained regression has a long history in statistics: Hildreth [73] considered least squares estimation (i.e., maximum likelihood estimation under Gaussian errors) of production functions under the natural assumption of nonincreasing returns (which implies that the production function is co”
A Nonparametric Approach to Measuring and Testing Curvature (2005, background): “The second category includes tests based on nonparametric estimation of functions subject to convex/concave restriction (e.g., Hildreth 1954; Mammen 1991; Wang 1992; Yatchew 1992).”
Shape restricted regression with random Bernstein polynomials (2007, background): “Starting from the classic works of Brunk [4] and Hildreth [ 17 ], there exists a large literature on the problem of estimating monotone, concave or convex regression functions.”
Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function (2010, background): “In the particular case of convex regression, Hanson and Pledger (1976) proved the consistency of the least squares estimator introduced in Hildreth (1954).”