Applications of Nonparametric Theory

Abstract

Recent developments in the nonparametric approach to efficiency have led to an upsurge of empirical and illustrative applications. Although Farrell started the nonparametric approach in the context of agricultural production data, the data envelopment analysis (DEA) initiated it as a tool for evaluating managerial efficiency. Since it has shadow price implications, it has important role in resource allocation models for economic development and international trade. The stochastic aspects of nonparametric theory, which are currently under intensive research efforts have important connections with the parametric and nonparametric models in the theory of stochastic programming. Treatment of risk and uncertainty, efficiency under incomplete information and the specification of the dynamic efficiency frontier under conditions of uncertainty regarding future demand are some of the major research areas where more applied work is forthcoming. Finally, the DEA approach through its emphasis on the data structure and their heterogeneity has opened up the broader question: how to integrate other data-based techniques with the nonparametric theory of the DEA model? We have already discussed in earlier chapters the use of such data-based techniques as nonparametric regression, influence curve approach and the bootstrap techniques. The use of entropy as an information-theoretic measure of data analysis comes readily to mind in this connection. Although entropy maximization has been related to statistical estimation theory, through Fisher’s information matrix, Kullback’s discrimination information and Akaike’s information criterion, its role in DEA model has yet not been explored.