Statistical Inference in high dimensional DEA model

Abstract

The paper aims to find a methodology to perform statistical inference for the estimation of efficiencies in the high dimensional data envelopment analysis (DEA) framework. This begins with the examination on the statistical model of the point estimator (mPCA-DEA) that eases the curse of dimensionality. To estimate the asymptotic distribution of mPCA-DEA, a double-smooth bootstrap method is adapted. To avoid unnecessary computational burden, an independence test in the distribution of efficiency is applied before bootstrapping the efficiency estimates. A numerical illustration with Malaysia car market data is used to demonstrate the methodology. It is shown that when the independence assumption holds, a double-smooth homogeneous bootstrap gives efficient inference. On the other hand, the heterogeneous bootstrap susceptibly identifies the outliers and the facets of frontier that are less dense when the independence assumption fails. These results substantiate the need to examine the asymptotic distribution of the mPCA-DEA estimator in the high dimensional framework so much so to provide meaningful interpretations. Nonetheless, the proposed methodology cannot totally overcome the curse of dimensionality in the nonparametric estimator. To further improve the estimation quality, researchers are encouraged to curtail the attributes or increase the sample size.