Nonparametric Frontier Estimation from Noisy Data
A new nonparametric estimator of production frontiers is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied using simulated data.
KeywordsData Envelopment Analysis Survival Function Production Unit Consistent Estimator Production Frontier
This work was supported by the “Agence National de la Recherche” under contract ANR-09-JCJC-0124-01 and by the IAP research network nr P6/03 of the Belgian Government (Belgian Science Policy). Comments from Ingrid Van Keilegom and an anonymous referee were most helpful to improve the final version of the manuscript. The usual disclaimer applies.
- Daouia, A., Florens, J., & Simar, L. (2009). Regularization in nonparametric frontier estimators (Discussion Paper No. 0922). Université catholique de Louvain, Belgium: Institut de statistique, biostatistique et sciences actuarielles.Google Scholar
- De Borger, B., Kerstens, K., Moesen, W., & Vanneste, J. (1994). A non-parametric free disposal hull (FDH) approach to technical efficiency: an illustration of radial and graph efficiency measures and some sensitivity results. Swiss Journal of Economics and Statistics, 130, 647–667.Google Scholar
- Deprins, D., Simar, L., & Tulkens, H. (1984). Measuring labor inefficiency in post offices. In M. Marchand, P. Pestieau, & H. Tulkens (Eds.), The performance of public enterprises: Concepts and measurements (pp. 243–267). Amsterdam: North-Holland.Google Scholar
- Färe, R., Grosskopf, S., & Knox Lovell, C. (1985). The measurements of efficiency of production (Vol. 6). New York: Springer.Google Scholar
- Johannes, J., & Schwarz, M. (2009). Adaptive circular deconvolution by model selection under unknown error distribution (Discussion Paper No. 0931). Université catholique de Louvain, Belgium: Institut de statistique, biostatistique et sciences actuarielles.Google Scholar
- Johannes, J., Van Bellegem, S., & Vanhems, A. (2010). Convergence rates for ill-posed inverse problems with an unknown operator. Econometric Theory. (forthcoming)Google Scholar
- Meister, A. (2007). Deconvolving compactly supported densities. Mathematical Methods in Statistics, 16, 195–211.Google Scholar