Penalized Likelihood-type Estimators for Generalized Nonparametric Regression

Journal of Multivariate Analysis

Volumn 56, Issue 2, 1996, Pages 185-206

  Cox, Dennis D ^a   Sullivan, Finbarr ^a  

^a NONE

Author keywords

Maximum penalized likelihood; Multiple classification; Non parametric aggression; Rates of convergence; Smoothing splines

Indexed keywords

EID: 0030076461     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1996.0010     Document Type: Article

References (26)

1. [1] ANTONIADIS, A., AND GREGOIRE, G. (1990). Penalized likelihood estimation for rates with censored survival data. Scand. J. Statist. 17 43-63.
2. [2] ADAMS, R. (1975). Sobolev Spaces. Academic Press, New York, 1975.
3. [3] BACCHETTI, P., AND JEWELL, N. P. (1991). Nonparametric estimation of the incubation period of AIDS based on a prevalent cohort with unknown infection times. Biometrics 47 947-960.
4. [4] BICKEL, P., AND DOKSUM, K. (1978). Mathematical Statistics. Holden-Day, San Francisco.
5. [5] CHEN, Z. (1991). Interaction spline models and their convergence rates. Ann. Statist. 19 1855-1868.
6. [6] Cox, D. D., AND O'SULLIVAN, F. (1990). Asymptotic analysis of penalized likelihood and related estimators. Ann. Statist. 18 1676-1695.
7. [7] Cox, D. D., AND O'SULLIVAN, F. (1994). On the Sobolev class of a composite function. Proc. Amer. Math. Soc. 122 727-732.
8. [8] Cox, D. D. (1984). Multivariate smoothing spline functions. SIAM J. Numer. Anal. 21 789-813.
9. [9] Cox, D. D. (1988). Approximation of method of regularization estimators. Ann. Statist. 16 694-694.
10. [10] CRAMER, H. (1946). Mathematical Methods of Statistics. Princeton Univ. Press, Princeton, NJ.
11. [11] GOOD, I. J., AND GASKINS, R. A. (1971). Non-parametric roughness penalties for probability densities. Biometrika 58 255-277.
12. [12] GREEN, P. J. (1990). On the use of the EM algorithm for penalized likelihood estimation. J. Roy. Statist. Soc. B 52 443-452.
13. [13] HUBER, P. (1979). Robust smoothing. In Proc. ARO Workshop on Robustness in Statistics April 11-12, 1978 (R. L. Launer and D. S. Moore, Eds.). Academic Press, New York.
14. [14] HUBER P. (1981). Robust Statistics. Wiley, New York.
15. [15] KATO, T., AND PONCE, G. (1988). Commutator estimates and the Euler and Navier-Stokes equations. Comm. Pure Appl. Math. 41 891-907.
16. [16] MCCULLAGH, P., AND NELDER, J. A. (1983). Generalized Linear Models. Chapman & Hall, London.
17. [17] NATTERER, F. (1986). Mathematics of Computerized Tomography. Wiley, Chichester.
18. [18] OGATA, Y., IMOTO, M., AND KATSURA, K. (1991). 3-D spatial variation of b-values of magnitude-freqency distribution beneath the Kanto District, Japan. Geophys. J. Roy. Astron. Soc. 104 135-146.
19. [19] O'SULLIVAN, F. (1993). Smooth mixture estimation for multi-channel image data. J. Amer. Statist. Assoc. 88 209-220.
20. [20] RALL, L. B. (1969). Computational Solution Nonlinear Operator Equations. Wiley, New York.
21. [21] SILVERMAN, B. W. (1985). Penalized maximum likelihood estimation. Encyclopedia statist. Sci. 6 664-667.
22. [22] STRICHARTZ, R. (1967). Multipliers in fractional Sobolev spaces. J. Math. Mech. 16 1031-1060.
23. [23] TRIEBEL, H. (1978). Interpolation Theory Function Spaces Differential Operators. North-Holland, New York.
24. [24] VILLALOBOS, M. A., AND WAHBA, G. (1983). Multivariate thin plate spline estimates for the posterior probabilities in the classification problem. Comm. Statist. A 12 1449-1479.
25. [25] WAHBA, G. (1990). Spline Models in Statistics. CBMS Regional Conference Series in Applied Mathematics, SIAM, Philadelphia.
26. [26] WEINBERGER, H. F. (1974). Variational Methods for Eigenvalue Approximation. CBMS Regional Conference Series in Applied Mathematics, Vol. 15. SIAM, Philadelphia.