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Uniform Convergence and Rate Adaptive Estimation of a Convex Function
Adaptive estimate B-splines convex regression minimax risk
2012/5/9
This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates vario...
Vertical Developments of a Convex Function
Convex analysis second-order derivative approximate subdifferential semidefinite programming
2009/1/22
In this paper we compare two different approaches to analyse the second-order behaviour of a convex function. The first one is classical, we call it the horizontal approach; the second one is more rec...
Inequalities Involving a Logarithmically Convex Function and Their Applications to Special Functions
Logarithmically convex functions inequalities gamma function Riemann's zeta function complete elliptic integrals of the first kind
2008/7/1
Inequalities Involving a Logarithmically Convex Function and Their Applications to Special Functions.
Estimation of the Derivative of the Convex Function by Means of its Uniform Approximation
Convex function Energy estimate Left-derivative Lower convex envelope Hedging strategies the American contingent claims
2008/7/1
Suppose given the uniform approximation to the unknown convex function on a bounded interval. Starting from it the objective is to estimate the derivative of the unknown convex function. We propose th...