×

Semiparametric stochastic frontier models for clustered data. (English) Zbl 1247.62114

Summary: The mixed model approach to semiparametric regression is considered for stochastic frontier models, with focus on clustered data. Standard assumptions about the model component representing the inefficiency effect lead to a closed skew normal distribution for the response. Model parameters are estimated by a generalization of restricted maximum likelihood, and random effects are estimated by an orthodox best linear unbiased prediction procedure. The method is assessed by means of Monte Carlo studies, and illustrated by an empirical application on hospital productivity.

MSC:

62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
65C05 Monte Carlo methods
62H30 Classification and discrimination; cluster analysis (statistical aspects)

Software:

R; Orthants; SemiPar; WinBUGS
Full Text: DOI

References:

[1] Aigner, D. J.; Lovell, C. A.K.; Schmidt, P., Formulation and estimation of stochastic frontier production function models, J. Econometrics, 6, 21-37 (1977) · Zbl 0366.90026
[2] Arellano-Valle, R. B.; Azzalini, A., On the unification of families of skew-normal distributions, Scand. J. Statist., 33, 561-574 (2006) · Zbl 1117.62051
[3] Bilodeau, D.; Crémieux, P.; Jaumard, B.; Ouellette, P.; Vovor, T., Measuring hospital performance in the presence of quasi-fixed inputs: an analysis of Québec hospitals, J. Prod. Anal., 21, 183-199 (2004)
[4] Botts, C. H.; Daniels, M. J., A flexible approach to Bayesian multiple curve fitting, Comput. Statist. Data Anal., 52, 5100-5120 (2008) · Zbl 1452.62035
[5] Caudill, S. B.; Ford, J. M.; Gropper, D. M., Frontier estimation and firm-specific inefficiency measures in the presence of heteroscedasticity, J. Bus. Econom. Statist., 13, 105-111 (1995)
[6] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, European J. Oper. Res., 2, 429-444 (1978) · Zbl 0416.90080
[7] Craig, P., A new reconstruction of multivariate normal orthant probabilities, J. Roy. Statist. Soc. Ser. B, 70, 227-243 (2008) · Zbl 05563352
[8] Crainiceanu, C.; Ruppert, D.; Wand, M. P., Bayesian analysis for penalized spline regression using WinBUGS, J. Statist. Softw., 14, 14 (2005)
[9] Deprins, D.; Simar, L.; Tulkens, H., Measuring labor efficiency in post offices, (Marchand, M.; Pestieau, P.; Tulkens, H., The Performance of Public Enterprises: Concepts and Measurements (1984), North-Holland: North-Holland Amsterdam), 243-267
[10] Domínguez-Molina, J. A.; González-Farías, G.; Ramos-Quiroga, R., Skew normality in stochastic frontier analysis, (Genton, M. G., Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality (2004), Chapman and Hall/CRC: Chapman and Hall/CRC Boca Raton), 223-241
[11] Fan, Y. Q.; Li, Q.; Weersink, A., Semiparametric estimation of stochastic production frontier models, J. Bus. Econom. Statist., 14, 460-468 (1996)
[12] Farrell, M. J., The measurement of productive efficiency, J. Roy. Statist. Soc. Ser. A, 120, 253-281 (1957)
[13] Fields Development Team, 2006. fields: Tools for Spatial Data. National Center for Atmospheric Research, Boulder, CO. URL http://www.image.ucar.edu/Software/Fields; Fields Development Team, 2006. fields: Tools for Spatial Data. National Center for Atmospheric Research, Boulder, CO. URL http://www.image.ucar.edu/Software/Fields
[14] French, J. L.; Kammann, E. E.; Wand, M. P., Comment on paper by Ke and Wang, J. Amer. Statist. Assoc., 96, 1285-1288 (2001)
[15] Genz, A.; Bretz, F., Comparison of methods for the computation of multivariate \(t\) probabilities, J. Comput. Graph. Statist., 11, 950-971 (2002)
[16] González-Farías, G.; Domínguez-Molina, A.; Gupta, A. K., Additive properties of skew normal random vectors, J. Statist. Plann. Inference, 126, 521-534 (2004) · Zbl 1076.62052
[17] Greene, W., Fixed and random effects in stochastic frontier models, J. Prod. Anal., 23, 7-32 (2005)
[18] Greene, W., The econometric approach to efficiency analysis, (Fried, H. O.; Lovell, C. A.K.; Schmidt, S. S., The Measurement of Productive Efficiency and Productivity Growth (2008), Oxford University Press), 92-251
[19] Griffin, J. E.; Steel, M. F.J., Semiparametric Bayesian inference for stochastic frontier models, J. Econometrics, 123, 121-152 (2004) · Zbl 1328.62208
[20] Griffin, J. E.; Steel, M. F.J., Bayesian stochastic frontier analysis using WinBUGS, J. Prod. Anal., 27, 163-176 (2007)
[21] Henderson, D.J., Simar, L., (2005). A fully nonparametric stochastic frontier model for panel data. Discussion Paper 0525, Institut de Statistiqué, Universite Catholique de Louvain.; Henderson, D.J., Simar, L., (2005). A fully nonparametric stochastic frontier model for panel data. Discussion Paper 0525, Institut de Statistiqué, Universite Catholique de Louvain.
[22] Horrace, W. C.; Schmidt, P., Confidence statements for efficiency estimates from stochastic frontier models, J. Prod. Anal., 7, 257-282 (1996)
[23] Joe, H.; Nash, J. C., Numerical optimization and surface estimation with imprecise function evaluations, Stat. Comput., 13, 277-286 (2003)
[24] Johnson, M. E.; Moore, L. M.; Ylvisaker, D., Minimax and maximin distance designs, J. Statist. Plann. Inference, 26, 131-148 (1990)
[25] Kneip, A.; Simar, L., A general framework for frontier estimation with panel data, J. Prod. Anal., 7, 187-212 (1996)
[26] Kumbhakar, S. C.; Lovell, C. A.K., Stochastic Frontier Analysis (2000), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0968.62080
[27] Kumbhakar, S. C.; Park, B. U.; Simar, L.; Tsionas, E. G., Nonparametric stochastic frontiers: a local maximum likelihood approach, J. Econometrics, 137, 1-27 (2007) · Zbl 1360.62131
[28] Ma, R.; Jørgensen, B., Nested generalized linear mixed models: an orthodox best linear unbiased predictor approach, J. Roy. Statist. Soc. Ser. B, 69, 625-641 (2007) · Zbl 07555368
[29] Mammen, E.; Marron, J. S.; Turlach, B. A.; Wand, M. P., A general projection framework for constrained smoothing, Statist. Sci., 16, 232-248 (2001) · Zbl 1059.62535
[30] Martins-Filho, C.; Yao, F., Nonparametric frontier estimation via local linear regression, J. Econometrics, 141, 283-319 (2007) · Zbl 1418.62163
[31] McCullagh, P.; Nelder, J. A., Generalized linear models (1989), Chapman and Hall: Chapman and Hall London · Zbl 0744.62098
[32] Meeusen, W.; van Den Broeck, J., Efficiency estimation from Cobb-Douglas production functions with composed error, Internat. Econom. Rev., 18, 435-444 (1977) · Zbl 0366.90025
[33] Ngo, L.; Wand, M. P., Smoothing with mixed model software, J. Statist. Softw., 9, 1-54 (2004)
[34] Orea, L.; Kumbhakar, S. C., Efficiency measurement using a latent class stochastic frontier model, Empirical Econ., 29, 169-183 (2004)
[35] Park, B. U.; Simar, L., Efficient semiparametric estimation in a stochastic frontier model, J. Amer. Statist. Assoc., 89, 929-936 (1994) · Zbl 0804.62100
[36] R Development Core Team, 2009. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.; R Development Core Team, 2009. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
[37] Ruppert, D., Selecting the number of knots for penalized splines, J. Comput. Graph. Statist., 11, 735-757 (2002)
[38] Ruppert, D.; Wand, M. P.; Carroll, R. J., Semiparametric Regression (2003), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1038.62042
[39] Sándor, Z.; András, P., Alternative sampling methods for estimating multivariate normal probabilities, J. Econometrics, 120, 207-234 (2004) · Zbl 1282.62024
[40] Schmidt, P.; Sickles, R. C., Production frontiers and panel data, J. Bus. Econom. Statist., 2, 367-374 (1984)
[41] Searle, S. R.; Casella, G.; McCulloch, C. E., Variance Components (1992), Wiley: Wiley New York · Zbl 0850.62007
[42] Sena, V., Stochastic frontier estimation: a review of the software options, J. Appl. Econometrics, 14, 579-586 (1999)
[43] Sima, D. M.; Van Huffel, S., A class of template splines, Comput. Statist. Data Anal., 50, 3486-3499 (2006) · Zbl 1445.62084
[44] Simar, L.; Wilson, P. W., Statistical inference in nonparametric frontier models: the state of art, J. Prod. Anal., 13, 49-78 (2000)
[45] Simar, L.; Wilson, P. W., Estimation and inference in two-stage, semi-parametric models of production processes, J. Econometrics, 136, 31-64 (2007) · Zbl 1418.62535
[46] Skaug, H. J.; Fournier, D. A., Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models, Comput. Statist. Data Anal., 51, 699-709 (2006) · Zbl 1157.65317
[47] Tsionas, E. G., Stochastic frontier models with random coefficients, J. Appl. Econometrics., 17, 127-147 (2002)
[48] Wand, M. P., Semiparametric regression and graphical models, Aust. N. Z. J. Stat., 51, 9-41 (2009) · Zbl 1334.62012
[49] Wang, H-J., Heteroscedasticity and non-monotonic efficiency effects of a stochastic frontier model, J. Prod. Anal., 18, 241-253 (2002)
[50] Wang, W. S.; Schmidt, P., On the distribution of estimated technical efficiency in stochastic frontier models, J. Econometrics, 148, 36-45 (2009) · Zbl 1429.62703
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.