Representation theorem for convex nonparametric least squares

Econometrics Journal

Volumn 11, Issue 2, 2008, Pages 308-325

  Kuosmanen, Timo ^a  

^a FINNISH FOREST RESEARCH INSTITUTE   (Finland)

Author keywords

Concavity; Convexity; Curve fitting; Linear splines; Local linear approximation; Nonparametric methods; Regression analysis

Indexed keywords

EID: 47649105902     PISSN: 13684221     EISSN: 1368423X     Source Type: Journal    
DOI: 10.1111/j.1368-423X.2008.00239.x     Document Type: Article

References (37)

1. Afriat, S. N. (1967). The construction of a utility function from expenditure data. International Economic Review 8, 67-77.
2. Banker, R. D. and A. Maindiratta (1992). Maximum likelihood estimation of monotone and concave production frontiers. Journal of Productivity Analysis 3, 401-15.
3. Barlow, R. E., J. M. Bartholomew, J. M. Bremner and H. D. Brunk (1972). Statistical Inference under Order Restrictions. New York: John Wiley & Sons.
4. Deaton, A. (1986). Demand analysis. In Z. Griliches and M. D. Intriligator (Eds.), Handbook of Econometrics, Volume 3, 1767-839. Amsterdam: North Holland.
5. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics 7, 1-26.
6. Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. CBMS-NSF Regional Conference Series in Applied Mathematics 38. Philadelphia: Society for Industrial and Applied Mathematics.
7. Efron, B. and R. J. Tibshirani (1993). An Introduction to the Bootstrap. London: Chapman and Hall.
8. Fan, J. and W. Zhang (1999). Statistical estimation in varying coefficients models. Annals of Statistics 27, 1491-518.
9. Fraser, D. A. S. and H. Massam (1989). A mixed primal-dual bases algorithm for regression under inequality constraints: Application to concave regression. Scandinavian Journal of Statistics 16, 65-74.
10. Goldman, S. M. and P. A. Ruud (1995). Nonparametric multivariate regression subject to constraint. Working paper, University of California at Berkeley.
11. Greene, W. H. (2005). Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. Journal of Econometrics 126, 269-303.
12. Groeneboom, P., G. Jongbloed and J. A. Wellner (2001). Estimation of convex functions: Characterizations and asymptotic theory. Annals of Statistics 26, 1653-98.
13. Hanson, D. L. and G. Pledger (1976). Consistency in concave regression. Annals of Statistics 4, 1038-50.
14. Hildreth, C. (1954). Point estimates of ordinates of concave functions. Journal of the American Statistical Association 49, 598-619.
15. Kuosmanen, T. (2006). Stochastic nonparametric envelopment of data: Combining virtues of SFA and DEA in a unified framework. MTT Discussion Paper 3/2006, Helsinki.
16. Kuosmanen, T. and M. Kortelainen (2007). Stochastic nonparametric envelopment of data: Cross-sectional frontier estimation subject to shape constraints. Economics Discussion Paper #46, University of Joensuu.
17. Mammen, E. (1991). Nonparametric regression under qualitative smoothness assumptions. Annals of Statistics 19, 741-59.
18. Mammen, E. and C. Thomas-Agnan (1999). Smoothing splines and shape restrictions. Scandinavian Journal of Statistics 26, 239-52.
19. Matzkin, R. L. (1991). Semiparametric estimation of monotone and concave utility functions for polychotomous choice models. Econometrica 59, 1315-27.
20. Matzkin, R. L. (1992). Nonparametric and distribution-free estimation of the binary threshold crossing and the binary choice models. Econometrica 60, 239-70.
21. Matzkin, R. L. (1994). Restrictions of economic theory in nonparametric methods. In R. F. Engle and D.L McFadden (Eds.), Handbook of Econometrics, Volume 4, 2523-58. Amsterdam: Elsevier.
22. Meyer, M. C. (1999). An extension of the mixed primal-dual bases algorithm to the case of more constraints than dimensions. Journal of Statistical Planning and Inference 81, 13-31.
23. Meyer, M. C. (2003). A test for linear vs. convex regression function using shape-restricted regression. Biometrika 90, 223-32.
24. Meyer, M. C. (2006). Consistency and power in tests with shape-restricted alternatives. Journal of Statistical Planning and Inference 136, 3931-47.
25. Nemirovskii, A. S., B. T. Polyak and A. B. Tsybakov (1985). Rates of convergence of nonparametric estimates of maximum likelihood type. Problems of Information Transmission 21, 258-71.
26. Rockafellar, R. T. (1970). Convex Analysis. NJ: Princeton University Press.
27. Ruud, P. A. (1996). Restricted least squares subject to monotonicity and concavity constraints, Working paper. University of California at Berkeley.
28. Sasabuchi, S., M. Inutsuka and D. D. S. Kulatunga (1983). A multivariate version of isotonic regression. Biometrica 70, 465-72.
29. Varian, H. (1982). The nonparametric approach to demand analysis. Econometrica 50, 945-73.
30. Varian, H. (1984). The nonparametric approach to production analysis. Econometrica 52, 579-97.
31. Varian, H. (1985). Nonparametric analysis of optimizing behavior with measurement error. Journal of Econometrics 30, 445-58.
32. Wahba, G. (1990). Spline models for observational data. CBMS-NSF Regional Conference Series in Applied Mathematics 59. Philadelphia: Society for Industrial and Applied Mathematics.
33. Wu, C. F. (1982). Some algorithms for concave and isotonic regression. TIMS Studies in Management Science 19, 105-16.
34. Yatchew, A. J. (1998). Nonparametric regression techniques in economics. Journal of Economic Literature 36, 669-721.
35. Yatchew, A. J. (2003). Semiparametric Regression for the Applied Econometrician. Cambridge: Cambridge University Press.
36. Yatchew, A. J. and L. Bos (1997). Nonparametric regression and testing in economic models. Journal of Quantitative Economics 13, 81-131.
37. Yatchew, A. J. and W. Härdle (2003). Nonparametric state price density estimation using constrained least squares and the bootstrap. Journal of Econometrics, 133, 579-599.