Estimation of non-sharp support boundaries
Journal of Multivariate Analysis
On the estimation of a support curve of indeterminate sharpness
Journal of Multivariate Analysis
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Clustering Algorithms
MiniMax Methods for Image Reconstruction
MiniMax Methods for Image Reconstruction
L1-Optimal Nonparametric Frontier Estimation via Linear Programming
Automation and Remote Control
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A new method for estimating the frontier of a set of points (or a support, in other words) is proposed. The estimates are defined as kernel functions covering all the points and whose associated support is of smallest surface. They are written as linear combinations of kernel functions applied to the points of the sample. The weights of the linear combination are then computed by solving a linear programming problem. In the general case, the solution of the optimization problem is sparse, that is, only a few coefficients are non zero. The corresponding points play the role of support vectors in the statistical learning theory. The L1-norm for the error of estimation is shown to be almost surely converging to zero, and the rate of convergence is provided.