Separating and Supporting Hyperplanes

2011 ◽  
pp. 213-229
Author(s):  
Jean Gallier
Keyword(s):  
Supporting Hyperplanes

Interval Predictor based on Supporting Hyperplanes

2018 ◽  
Author(s):  
J.M. Bravo ◽  
E. Cojocaru ◽  
M. Vasallo ◽  
T. Alamo
Keyword(s):  
Supporting Hyperplanes

scholarly journals Recent Applications of Nonparametric Programming Methods

1992 ◽  
Vol 21 (2) ◽  
pp. 113-120 ◽  
Author(s):  
Hyunok Lee
Keyword(s):  
Convex Sets ◽  
Revealed Preference ◽  
Production Data ◽  
Nonparametric Analysis ◽  
Preference Analysis ◽  
Supporting Hyperplanes ◽  
Linear Programming Methods ◽  
Consumption Data ◽  
Nonparametric Techniques ◽  
Revealed Preference Analysis

Nonparametric techniques have recently come into vogue in agricultural economics: Applications abound in both consumer and producer models of the agricultural economy. Moreover, several distinct approaches to nonparametric analysis exist. There are nonparametric statistical techniques, semiparametric estimation techniques, nonparametric revealed-preference analysis of consumption data, and nonparametric analysis of production data. Both revealed-preference analysis and nonparametric analysis of production data rely on the basic fact, which provides the foundation for much of modern duality theory, that convex sets can be completely characterized by their supporting hyperplanes. This observation allows one to apply simple mathematical programming (in particular, linear programming) methods to analyze production and consumption data. My task today is to provide an overview of nonparametric programming approaches to production data. Thus, I will not address any of the other topics cited above. However, I would be remiss if I did not mention the close connection between these subject areas and what I intend to survey today. Moreover, one should also recognize that very closely related to the literature on nonparametric programming analysis of production data are the fields of estimation of efficiency frontier via statistical methods. (A useful survey here is Lovell and Schmidt).

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