Functional estimation under shape constraints

Journal of Nonparametric Statistics

Volumn 6, Issue 1, 1996, Pages 69-89

  Delecroix, Michel ^a   Simioni, Michel ^b   Thomas Agnan, Christine ^c  

^a CREST   (France)

^b CEMAGREF   (France)

^c TOULOUSE SCHOOL OF ECONOMICS   (France)

Author keywords

Convex optimization; Convexity constraints; Kernel smoother; Nonparametric regression; Reproducing kernels

Indexed keywords

EID: 0001981258     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485259608832664     Document Type: Article

References (32)

1. Adams R. A., (1975). Sobolev spaces, Academic Press, Inc, Harcourt Brace Jovanovich Publishers.
2. m splines for noisy data, Numerische Mathematik 66, pp. 281-294.
3. Aronszajn N. (1943). Theorie des noyaux reproduisants et applications, Proceedings of the Cambridge Philosophical Society 39, pp. 133-153.
4. Birgé L. (1987). Estimating a density under order restrictions, Annals of Statistics 15, pp. 995-1012.
5. Chui C. K., Deutsch F. and Ward J. D. (1992). Constrained Best Approximation in Hilbert Space, II, Journal of Approximation Theory 71, pp. 213-238.
6. Cox D. (1984). Multivariate smoothing spline functions, SIAM Journal on Numerical Analysis, 21, pp. 789-813.
7. Cuevas A. and Gonzalez-Manteiga W. (1991). Data-driven smoothing based on convexity properties, in: Nonparametric Functional Estimation and Related Topics, G. G. Roussas eds, pp. 225-240, Kluwer Academic Pub.
8. Delecroix M. and Simioni M. (1993). Cost functions and optimizing behavior: a nonparametric approach, mimeo INRA.
9. Delecroix M., Simioni M. and Thomas-Agnan C. (1993). A shape constrained smoother: simulation study, Computational Statistics 10, pp. 155-175.
10. Dierckx P. (1980). An Algorithm for cubic spline fitting with convexity constraints. Computing 24, pp. 349-371.
11. Diewert W. E. and Wales T. J. (1987). Flexible functional forms and global curvature conditions, Econometrica, 55, no1, 43-68.
12. Gallant A. R. and Golub G. H. (1984). Imposing curvature restrictions on flexible functional forms, J. of Econometrics, 26, pp. 295-321.
13. Gasser T. and Muller H. G. (1979). Kernel estimation of regression functions, in: Smoothing techniques for curve estimation, T. Gasser and M. Rosenblatt eds, SpringerVerlag, Heidelberg.
14. Härdle W. (1990). Applied nonparametric regression, Econometric Society Monographs, University Press, Cambridge.
15. Lau L. (1990). Testing and imposing monotonicity, convexity and quasi-convexity, in M. A. Fuss and D. Mc Fadden eds, Production economics: a dual approach to theory and applications, North Holland, Amsterdam, 2, pp. 409-445.
16. Laurent P. J., An algorithm for the computation of spline functions with inequality constraints, technical report I. M. A. G. 335, Grenoble, France.
17. Mack Y. P. and Müller H. G. (1989). Convolution type estimators for nonparametric regression, Statistics and Probability Letters, pp. 229-239.
18. Mammen E. (1991). Nonparametric regression under qualitative smoothness assumptions, The Annals of Statistics, 19, pp. 741-759.
19. Mammen E. (1991). Estimating a smooth monotone regression function, The Annals of Statistics, 19, pp. 724-740.
20. Micchelli C. A. and Utreras F. I. (1988) Smoothing and interpolation in a convex subset of a Hilbert space, SIAM Journal of Scientific and Statistical Computing 9, pp. 728-747.
21. Mukerjee H. (1988). Monotone nonparametric regression, The Annals of Statistics 16, pp. 741-750.
22. Muller H-G and Schmitt T. (1988). Kernel and probit estimates in quantal bioassay, J.A.S.A., 83, pp. 750-759.
23. Priestley M. B. and Chao M. T. (1972). Nonparametric function fitting, Journal of the Royal Statistical Society B 34, pp. 385-392.
24. Ramsay J. O. (1988). Monotone regression splines in action, Statistical Science, 3, pp. 425-461.
25. Robertson T., Dykstra R. L. and Wright F. T. (1988). Order restricted Statistical Inference, Wiley.
26. Rockafeller R. T. (1970). Convex analysis, Princeton University Press, Princeton, New Jersey.
27. Thomas-Agnan C. (1993). Computing Reproducing kernels for statistical Applications, Technical report 908, University of Wisconsin, Madison.
28. Utreras F. (1985). Smoothing Noisy Data Under Monotonicity Constraints: Existence, Characterization and Convergence Rates, Numerische Mathematik 47, pp. 611-625.
29. Villalobos M. and Wahba G. (1987). Inequality Constrained Multivariate Smoothing Splines with Applications to the Estimation of Posterior Probabilities, Journal of the American Statistical Association 82, pp. 239-248.
30. Wahba G. (1990). Spline models for observational data, SIAM pub.
31. Walter G. G. and Blum J. R. (1984). A simple solution to a nonparametric maximum likelihood estimation problem, The Annals of Statistics, 12, pp. 372-379.
32. Wright I. W. and Wegman E. J. (1980). Isotonic, convex and related splines, The Annals of Statistics, 8, 5, pp. 1023-1035.