On nonparametric estimation of intercept and slope distributions in random coefficient regression

Annals of Statistics

Volumn 24, Issue 6, 1996, Pages 2569-2592

  Beran, Rudolf ^a   Feuerverger, Andrey ^c   Hall, Peter ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Characteristic function; Computerized tomography; Local linear regression; Projection slice theorem; Radon transform; Tapered fourier inversion

Indexed keywords

EID: 0030335136     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032181170     Document Type: Article

References (17)

1. BECKER, R. A., CHAMBERS J. M. and WILKS, A. R. (1988). The New S Language. Wadsworth and Brooks/Cole, Pacific Grove, CA.
2. BERAN, R. J. and HALL, P. (1992). Estimating coefficient distributions in random coefficient regression. Ann. Statist. 20 1110-1119.
3. BERAN, R. J. and MILLAR, P. W. (1994). Minimum distance estimation in random coefficient regression models. Ann. Statist. 22 1976-1992.
4. CARROLL, R. J. and HALL, P. (1988). Optimal rates of convergence for deconvolving a density. J. Amer. Statist. Assoc. 83 1184-1186.
5. DEANS, S. R. (1983). The Radon Transform and Some of Its Applications. Wiley, New York.
6. DEVANEY, A. J. (1989). The limited-view problem in diffraction tomography. Inverse Problems 5 501-521.
7. FAN, J. (1991). On the optimal rate of convergence for nonparametric deconvolution problems. Ann. Statist. 19 1257-1272.
8. FAN, J. (1992). Design-adaptive nonparametric regression. J. Amer. Statist. Assoc. 87 998-1004.
9. FAN, J. (1993). Local linear smoothers and their minimax efficiency. Ann. Statist. 21 196-216.
10. HALL, P., MARRON, S. J., NEUMANN, M. H. and TITTERINGTON, D. M. (1994). Curve estimation when the design density is low. Ann. Statist. To appear.
11. LIU, J. (1994). Minimum distance procedures in nonlinear random coefficient models. Ph.D. dissertation, Dept. Statistics, Univ. California, Berkeley.
12. LONGFORD, N. T. (1993). Random Coefficient Models. Oxford Univ. Press.
13. NICHOLLS, D. F. and PAGAN, A. R. (1985). Varying coefficient regression. In Handbook of Statistics (E. J. Hannan, P. R. Krishnaiah and M. M. Rao, eds.) 5. North-Holland, Amsterdam.
14. RAJ, B. and ULLAH, A. (1981). Econometrics, A Varying Coefficients Approach. Croom-Helm, London.
15. SHEPP, L. A. and KRUSKAL, J. B. (1979). Computerized tomography: the new medical X-ray technology. Amer. Math. Monthly 85 420-439.
16. SILVERMAN, B. W., JONES, M. C., WILSON, J. D. and NYCHKA, D. W. (1990). A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography. J. Roy. Statist. Soc. Ser. B 52 271-324.
17. STIGLER, S. M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press, Cambridge, MA.