Optimal Bandwidth Selection for Conditional Efficiency Measures: a Data-driven Approach
AbstractIn productivity analysis an important issue is to detect how external (environmental) factors, exogenous to the production process and not under the control of the producer, might influence the production process and the resulting efficiency of the firms. Most of the traditional approaches proposed in the literature have serious drawbacks. An alternative approach is to describe the production process as being conditioned by a given value of the environmental variables (Cazals, Florens and Simar, 2002, Daraio and Simar, 2005). This defines conditional efficiency measures where the production set in the input × output space may depend on the value of the external variables. The statistical properties of nonparametric estimators of these conditional measures are now established (Jeong, Park and Simar, 2008). These involve the estimation of a nonstandard conditional distribution function which requires the specification of a smoothing parameter (a bandwidth). So far, only the asymptotic optimal order of this bandwidth has been established. This is of little interest for the practitioner. In this paper we fill this gap and we propose a data-driven technique for selecting this parameter in practice. The approach, based on a Least Squares Cross Validation procedure (LSCV), provides an optimal bandwidth that minimizes an appropriate integrated Mean Squared Error (MSE). The method is carefully described and exemplified with some simulated data with univariate and multivariate environmental factors. An application on real data (performances of Mutual Funds) illustrates how this new optimal method of bandwidth selection outperforms former methods.
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Bibliographic InfoPaper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2008/22.
Date of creation: 24 Oct 2008
Date of revision:
Nonparametric efficiency estimation; conditional efficiency measures; environmental factors; conditional distribution function; bandwidth.;
Other versions of this item:
- Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 633-640, March.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- D20 - Microeconomics - - Production and Organizations - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-10-28 (All new papers)
- NEP-ECM-2008-10-28 (Econometrics)
- NEP-EFF-2008-10-28 (Efficiency & Productivity)
- NEP-ENV-2008-10-28 (Environmental Economics)
- NEP-ORE-2008-10-28 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cinzia Daraio & Leopold Simar, 2003.
"Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach,"
LEM Papers Series
2003/17, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
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Elsevier, vol. 146(1), pages 185-198, September.
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- Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
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- Simar, Léopold, 2003.
"How to Improve the Performances of DEA/FDH Estimators in the Presence of Noise?,"
SFB 373 Discussion Papers
2003,33, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Léopold Simar, 2007. "How to improve the performances of DEA/FDH estimators in the presence of noise?," Journal of Productivity Analysis, Springer, vol. 28(3), pages 183-201, December.
- Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
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