Penalized quasi-likelihood estimation in partial linear models

Annals of Statistics

Volumn 25, Issue 3, 1997, Pages 1014-1035

  Mammen, Enno ^a   Van De Geer, Sara ^b  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Asymptotic normality; Penalized likelihood; Rates of convergence

Indexed keywords

EID: 0031508286     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1069362736     Document Type: Article

References (37)

1. AGMON, S. (1965). Lectures on Elliptic Boundary Value Problems, van Nostrand, Princeton, NJ.
2. BERAN, R. (1986). Comment on "Jackknife, bootstrap, and other resampling methods in regression analysis" by C. F. J. Wu. Ann. Statist. 14 1295-1298.
3. BIRGÉ, L. and MASSART, P. (1991). Rates of convergence for minimum contrast estimators. Technical Report 140, Univ. Paris 6.
4. p. Mat. Sbornik 73 295-317.
5. CHEN, H. (1988). Convergence rates for parametric components in a partly linear model. Ann. Statist. 16 136-146.
6. Cox, D. D., KOH, E., WAHBA, G. and YANDELL, B. S. (1988). Testing the (parametric) null model hypothesis in (semiparametric) partial and generalized spline models. Ann. Statist. 16 113-119.
7. Cox, D. D. and O'SULLIVAN, F. (1990). Asymptotic analysis of penalized likelihood and related estimators. Ann. Statist. 18 1676-1695.
8. DUDLEY, R. M. (1984). A course on empirical processes. Ecole d'Eté de Probabilités de St. Flour. Lecture Notes in Math. 1882 1-122. Springer, Berlin.
9. FAN, J., HECKMAN, N. E. and WAND, M. P. (1995). Local polynomial regression for generalized linear models and quasi-likelihood functions. J. Amer. Statist. Assoc. 90 141-150.
10. GINÉ, E. and ZINN, J. (1984). On the central limit theorem for empirical processes. Ann. Probab. 12 929-989.
11. GREEN, P. J. (1987). Penalized likelihood for general semi-parametric regression models. Internat. Statist. Rev. 55 245-260.
12. GREEN, P. J. and YANDELL, B. (1985). Semi-parametric generalized linear models. Proceedings Second International GLIM Conference. Lecture Notes in Statist. 32 44-55. Springer, New York.
13. Gu, C. (1990). Adaptive spline smoothing in non-Gaussian regression models. J. Amer. Statist. Assoc. 85 801-807.
14. Gu, C. (1992). Cross-validating non-Gaussian data. J. Comput. Graph. Statist. 1 169-179.
15. HARDLE, W. and MAMMEN, E. (1993). Comparing nonparametric versus parametric regression fits. Ann. Statist. 21 1926-1947.
16. MAMMEN, E. (1992). When Does Bootstrap Work: Asymptotic Results and Simulations. Lecture Notes in Statist. 77. Springer, Berlin.
17. McCULLAGH, P. (1983). Quasi-likelihood functions. Ann. Statist. 11 59-67.
18. McCuLLAGH, P. and NELDER, J. A. (1989). Generalized Linear Models, 2nd ed. Chapman and Hall, London.
19. ODEN, J. T. and REDDY, J. N. (1976). An Introduction to the Mathematical Theory of Finite Elements. Wiley, New York.
20. 2 bracketing. Ann. Probab. 15 897-919.
21. O'SULLIVAN, F., YANDELL, B. and RAYNOR, W. (1986). Automatic smoothing of regression functions in generalized linear models. J. Amer. Statist. Assoc. 81 96-103.
22. POLLARD, D. (1984). Convergence of Stochastic Processes. Springer, New York.
23. POLLARD, D. (1990). Empirical Processes: Theory and Applications. IMS, Hayward, CA.
24. RICE, J. (1986). Convergence rates for partially splined models. Statist. Probab. Lett. 4 203-208.
25. RICE, J. and ROSENBLATT, M. (1981). Integrated mean square error of a smoothing spline. J. Approx. Theory 33 353-369.
26. SEVERINI, T. A. and STANISWALIS, J. G. (1994). Quasi-likelihood estimation in semiparametric models. J. Amer. Statist. Assoc. 89 501-511.
27. SILVERMAN, B. W. (1985). Some aspects of the spline smoothing approach to nonparametric regression curve fitting (with discussion). J. Roy. Statist. Soc. Ser. B 47 1-52.
28. SPECKMAN, P. (1988). Kernel smoothing in partial linear models. J. Roy. Statist. Soc. Ser. B 50 413-436.
29. UTRERAS, F. (1985). Smoothing noisy data under monotonicity constraints: existence, characterization and convergence rates. Numer. Math. 47 611-625.
30. VAN DE GEER, S. (1988). Regression analysis and empirical processes. CWI Tract 45. Centre for Mathematics and Computer Science, Amsterdam.
31. VAN DE GEER, S. (1990). Estimating a regression function. Ann. Statist. 18 907-924.
32. VAN DE GEER, S. (1995). A maximal inequality for the empirical process. Technical Report TW 95-05, Univ. Leiden.
33. WAHBA, G. (1984). Partial spline models for the semi-parametric estimation of functions of several variables. In Statistical Analysis of Time Series 319-329. Institute of Statistical Mathematics, Tokyo.
34. WAHBA, G. (1990). Spline Models for Observational Data. SIAM, Philidelphia.
35. WEDDERBURN, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61 439-447.
36. Wu, C F. J. (1986). Jackknife, bootstrap, and other resampling methods in regression analysis. Ann. Statist. 14 1261-1350.
37. XIANG, D. and WAHBA, W. (1995). Testing the generalized linear model null hypothesis versus "smooth" alternatives. Technical Report 953, Univ. Wisconsin-Madison.