Monotone b-spline smoothing

Journal of the American Statistical Association

Volumn 93, Issue 442, 1998, Pages 643-650

  He, Xuming ^a   Shi, Peide ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b PEKING UNIVERSITY   (China)

Author keywords

B spline; Constraints; Information criterion; Least absolute deviation; Linear programming; Median; Monotone smoothing; Quantiles

Indexed keywords

EID: 0032390646     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1998.10473717     Document Type: Article

References (30)

1. Akaike, H. (1973), "Information Theory and an Extension of the Maximum Likelihood Principle," in Second International Symposium on Information Theory, eds. B. N. Petrov and F. Csaki, Budapest: Akademia Kiado, pp. 267-281.
2. Dierckx, P. (1993), Curve and Surface Fitting With Splines. Oxford, U.K.: Clarendon Press.
3. Dole, D. (1997), "Scatterplot Smoothing Subject to Monotonicity and Convexity," unpublished manuscript submitted to Journal of Business and Economic Statistics.
4. Friedman, J. H., and Silverman, B. W. (1989), "Flexible Parsimonious Smoothing and Additive Modeling" (with discussion). Technometrics, 31, 3-21.
5. Friedman, J. H., and Tibshirani, R. (1984), "The Monotone Smoothing of Scatterplots," Technometrics, 26, 243-250.
6. Hardle, W. (1990), Applied Nonparametric Regression, Cambridge, U.K.: Cambridge University Press.
7. Hawkins, D. M. (1994), "Fitting Monotonic Polynomials to Data," Computational Statistics Quarterly, 9, 233-247.
8. He, X. (in press), "Quantilc Curves Without Crossing," The American Statistician, 51, 186-192.
9. He, X., and Ng, P. (in press), "COS: Constrained Smoothing via Linear Programming," unpublished manuscript submitted to Computational Statistics.
10. He, X., and Shao, Q. M. (1996), "A General Bahadur Representation of M Estimators and Its Application to Linear Regression With Nonstochastic Designs," The Annals of Statistics, 24, 2608-2630.
11. He, X., and Shi, R (1994), "B-Spline Estimates of Conditional Quantile Functions," Nonparametric Statistics, 3, 299-308.
12. He, X., and Shi, R (1996), "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, 58, 162-181.
13. Jurekova, J. (1977), "Asymptotic Relations of M-Estimates and R-Estimates in Linear Regression Models. The Annals of Statistics, 5,464-472.
14. Kocnker, R., and Bassett, G. (1978), "Regression Quantiles," Economet-rica, 46. 33-50.
15. Koenker, R., Ng, P., and Portnoy, S. (1994). "Quantile Smoothing Splines," Biometrika, 81, 673-680.
16. Kooperberg, C., and Stone, C. J. (1992), "Logspline Density Estimation for Censored Data." Journal of Computational and Graphical Statistics, 1, 301-328.
17. Linhart, H., and Zucchini, W. (1986), Model Selection, New York: Wiley.
18. Mammen, E. (1991), "Estimating a Smooth Monotone Regression Function," The Annals of Statistics, 19, 724-740.
19. Mukerjee, H. (1988), "Monotone Nonparametric Regression," The Annals of Statistics, 16,741-750.
20. Ng, P. (1996), "An Algorithm for Quantile Smoothing Splines," Computational Statistics and Data Analysis, 2, 99-118.
21. Portnoy, S. (1997), "Local Asymptotics for Quantile Smoothing Splines," The Annals of Statistics, 25, 414-434.
22. Ramsay, J. (1988). "Monotone Regression Splines in Action." Statistical Science, 3, 425-441.
23. Ramsay, J (1998), "Estimating Smooth Monotone Functions." unpublished manuscript submitted to Journal of Royal Statistical Society, Ser. B.
24. Schumaker, L. L. (1981), Spline Functions, New York: Wiley.
25. Schumaker, L. L., and Utreras, F. I. (1990), "On Generalized Cross-Validation for Tensor Smoothing Splines," SIAM Journal of Scientific and Statistical Computing, 11, 713-731.
26. Shi, P. D., and Li, G. Y. (1995), "Global Rates of Convergence of B-Spline M-Estimates for Nonparametric Regression," Statistica Sinica, 5, 303-318.
27. Stone, C. (1982), "Optimal Global Rates of Convergence for Nonparametric Regression," The Annals of Statistics, 10, 1040-1053.
28. Villalobos, M., and Wahba, G. (1987), "Inequality-constrained Multivariate Smoothing Splines With Application to the Estimation of Posterior Probabilities," Journal of the American Statistical Association, 82, 239-248.
29. Wright, F. T. (1982), "Monotone Regression Estimates for Grouped Observations," The Annals of Statistics, 10, 278-286.
30. Wahba, G. (1988). "Comments on 'Monotone Regression Splines in Action' by J. Ramsay," Statistical Science, 3, 456-458.