A more efficient algorithm for Convex Nonparametric Least Squares

European Journal of Operational Research

Volumn 227, Issue 2, 2013, Pages 391-400

  Lee, Chia Yen ^a   Johnson, Andrew L ^b   Moreno Centeno, Erick ^b   Kuosmanen, Timo ^c  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b Department of Electrical and Computer Engineering   (United States)

^c HELSINKI SCHOOL OF ECONOMICS   (Finland)

Author keywords

Computational complexity; Convex Nonparametric Least Squares; Frontier estimation; Model reduction; Productive efficiency analysis

Indexed keywords

COMPUTATIONAL BURDEN; COMPUTATIONAL PERFORMANCE; CONVEX NONPARAMETRIC LEAST SQUARES; FRONTIER ESTIMATION; FUNCTIONAL FORMS; GENERIC ALGORITHM; MODEL REDUCTION; MONTE CARLO SIMULATION; NON-PARAMETRIC REGRESSION; PROBLEM SIZE; PRODUCTIVE EFFICIENCY ANALYSIS; SAMPLE SIZES; SMALL SAMPLES;

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER PROGRAMMING; MATHEMATICAL PROGRAMMING; MONTE CARLO METHODS; REGRESSION ANALYSIS;

PROBLEM SOLVING;

EID: 84873716417     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2012.11.054     Document Type: Article

References (43)

1. S.N. Afriat The construction of a utility function from expenditure data International Economic Review 8 1967 67 77
2. S. Afriat Efficiency estimation of production functions International Economic Review 13 1972 568 598
3. N. Aguilera, Forzani L.; and P. Morin On uniform consistent estimators for convex regression Journal of Nonparametric Statistics 23 4 2012 897 908
4. R.D. Banker, A. Charnes, and W.W. Cooper Some models for estimating technical and scale inefficiencies in data envelopment analysis Management Science 30 9 1984 1078 1092
5. G. Boyd, and R. Fare Measuring the efficiency of decision making units: a comment European Journal of Operational Research 15 1984 331 332
6. A. Charnes, and W.W. Cooper The non-Archimedean CCR ratio for efficiency analysis: a rejoinder to boyd and fare European Journal of Operational Research 15 1984 333 334
7. G.B. Dantzig, D.R. Fulkerson, and S.M. Johnson Solution of a large-scale traveling salesman problem Operations Research 2 1954 393 410
8. G.B. Dantzig, D.R. Fulkerson, and S.M. Johnson On a linear-programming combinatorial approach to the traveling-salesman problem Operations Research 7 1959 58 66
9. Du, P.; Parmeter, C.F.; Racine, J.S.; in press. Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints, Statistica Sinica.
10. J.H. Dulá An algorithm for data envelopment analysis INFORMS Journal on Computing 23 2 2011 284 296
11. R.L. Dykstra An algorithm for restricted least squares regression Journal of the American Statistical Association 78 384 1983 837 842
12. A. Fostel, H.E. Scarf, and M.J. Todd Two new proofs of Afriat's theorem Economic Theory 24 1 2004 211 219
13. D.A.S. Fraser, and H. Massam A mixed primal-dual bases algorithm for regression under inequality constraints: application to concave regression Scandinavian Journal of Statistics 16 1989 65 74
14. H.O. Fried, C.A.K. Lovell, and S.S. Schmidt The Measurement of Productive Efficiency and Productivity Growth 2008 Oxford University Press New York
15. Goldman, S.M.; Ruud, P.A.; 1993. Nonparametric Multivariate Regression Subject to Constraint. Technical Report 93-213, Department of Economics, University of California at Berkeley.
16. P. Groeneboom, G. Jongbloed, and J.A. Wellner Estimation of convex functions: characterizations and asymptotic theory Annals of Statistics 26 2001 1653 1698
17. Hannah, L.A.; Dunson, D.B.; 2012. Ensemble methods for convex regression with applications to geometric programming based circuit design. In: Proceedings of the 29th International Conference on Machine Learning, ICML, vol. 1, pp. 369-376.
18. D.L. Hanson, and G. Pledger Consistency in concave regression Annals of Statistics 4 6 1976 1038 1050
19. A. Henningsen, and C. Henning Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure Journal of Productivity Analysis 32 3 2009 217 229
20. C. Hildreth Point estimates of ordinates of concave functions Journal of the American Statistical Association 49 267 1954 598 619
21. A.L. Johnson, and T. Kuosmanen One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient, root-n consistent StoNEZD method Journal of Productivity Analysis 36 2 2011 219 230
22. A.L. Johnson, and T. Kuosmanen One-Stage and two-stage DEA estimation of the effects of contextual variables European Journal of Operational Research 220 2 2012 559 570
23. Johnson, A.L.; Ruggiero, J.; in press. Nonparametric measurement of productivity and efficiency in education. Annals of Operations Research.
24. J. Jondrow, C.A.K. Lovell, I.S. Materov, and P. Schmidt On the estimation of technical inefficiency in the stochastic frontier production function model Journal of Econometrics 19 2-3 1982 233 238
25. R.E. Just, and R.D. Pope Stochastic specification of production function and economic implications Journal of Econometrics 7 1 1978 67 86
26. T. Kuosmanen Representation theorem for convex nonparametric least squares Econometrics Journal 11 2008 308 325
27. T. Kuosmanen, and N. Kuosmanen Role of Benchmark Technology in Sustainable Value Analysis: an Application to Finnish Dairy Farms Agricultural and Food Science 18 3-4 2009 302 316
28. T. Kuosmanen Stochastic semi-nonparametric frontier estimation of electricity distribution networks: application of the StoNED method in the finnish regulatory model Energy Economics 34 2012 2189 2199
29. T. Kuosmanen, and A.L. Johnson Data envelopment analysis as nonparametric least-squares regression Operations Research 58 1 2010 149 160
30. T. Kuosmanen, and M. Kortelainen Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints Journal of Productivity Analysis 38 1 2012 11 28
31. E. Lim, and P.W. Glynn Consistency of multidimensional convex regression Operations Research 60 1 2012 196 208
32. E. Mammen Nonparametric regression under qualitative smoothness assumptions Annuals of Statistics 19 1991 741 759
33. E. Mammen, and C. Thomas-Agnan Smoothing splines and shape restrictions Scandinavian Journal of Statistics 26 1999 239 252
34. M. Mekaroonreung, and A.L. Johnson Estimating the Shadow Prices of SO2 and NOx for U. S. Coal Power Plants: a convex nonparametric least squares approach Energy Economics 34 3 2012 723 732
35. M.C. Meyer An extension of the mixed primal-dual bases algorithm to the case of more constraints than dimensions Journal of Statistical Planning and Inference 81 1999 13 31
36. B.N. Pshenichny, and M.Y. Danilin Numerical Methods in Extremal Problems 1978 Mir Publishers Moscow
37. Ruud, P.A.; 1995. Restricted Least Squares Subject to Monotonicity and Concavity Constraints. Working Paper, University of California at Berkeley.
38. E. Seijo, and B. Sen Nonparametric least squares estimation of a multivariate convex regression Annals Statistics 39 2012 1633 1657
39. H. Varian The nonparametric approach to demand analysis Econometrica 50 1982 945 973
40. H. Varian The nonparametric approach to production analysis Econometrica 52 1984 579 597
41. D.R. Wilhelmsen A nearest point algorithm for convex polyhedral cones and applications to positive linear approximation Mathematics of Computation 30 133 1976 48 57
42. C.F. Wu Some algorithms for concave and isotonic regression TIMS Studies in Management Science 19 1982 105 116
43. A. Yatchew Nonparametric regression techniques in economics Journal of Economic Literature 36 2 1998 669 721