L 1-optimal linear programming estimator for periodic frontier functions with Hölder continuous derivative
- 39 Downloads
We propose a new estimator based on a linear programming method for smooth frontiers of sample points on a plane. The derivative of the frontier function is supposed to be Hölder continuous. The estimator is defined as a linear combination of kernel functions being sufficiently regular, covering all the points and whose associated support is of smallest surface. The coefficients of the linear combination are computed by solving a linear programming problem. The L 1 error between the estimated and the true frontier function is shown to be almost surely converging to zero, and the rate of convergence is proved to be optimal.
KeywordsKernel Function Remote Control Lipschitz Constant Kernel Regression Planning Inference
Unable to display preview. Download preview PDF.
- 1.Deprins, D., Simar, L., and Tulkens, H., Measuring Labor Efficiency in Post Offices, in The Performance of Public Enterprises: Concepts and Measurements,Marchand, M., Pestieau, P., and Tulkens, H., Eds., Amsterdam: North-Holland, 1984, pp. 243–267.Google Scholar
- 18.Korostelev, A.P. and Tsybakov, A.B., Minimax Theory of Image Reconstruction, Lecture Notes Statist., vol. 82, New York: Springer-Verlag, 1993.Google Scholar
- 22.Girard, S., Guillou, A., and Stupfler, G., Uniform Strong Consistency of a Frontier Estimator Using Kernel Regression on High Order Moments, ESAIM: Probab. Statist., 2014 (to appear).Google Scholar