Maximum penalized likelihood estimation and smoothed EM algorithms for positive integral equations of the first kind

Numerical Functional Analysis and Optimization

Volumn 17, Issue 7-8, 1996, Pages 737-754

  Eggermont, P P B ^a   Lariccia, V N ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

EM algorithm; Integral equation of the first kind; Maximum penalized likelihood; Nonlinear smoothing; Regularization

Indexed keywords

EID: 0013228222     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630569608816722     Document Type: Article

References (19)

1. RA Adams, Sobolev spaces, Academic Press, New York, 1975.
2. LM Cruz-Orive, Distribution free estimation of sphere size distributions from slabs showing overprojection and truncation, with a, review of previous methods, J Microscopy 131 (1983), 265-290.
3. EB Davies, Heat kernels and spectral theory, Cambridge University Press, Cambridge, 1989.
4. PPB Eggermont, Nonlinear smoothing and the EM algorithm for positive integral equations of the first kind, Manuscript, University of Delaware (1992).
5. PPB Eggermont, and VN LaRiccia, Smoothed maximum likelihood density estimation for inverse problems, Ann Statist 23 (1996), 199-220.
6. IJ Good, and RA Gaskins, Nonparametric roughness penalties for probability densities, Biometrika 58 (1971), 255-277.
7. GH Hardy, JE Littlewood, and G Polya, Inequalities, Cambridge University Press, Cambridge, 1934.
8. T Kato, Perturbation theory for linear operators, Springer-Verlag, New York, 1976.
9. JHB Kemperman, On the optimum rate of transmitting information, Springer Lecture Notes in Mathematics 23 (1967), 126-169.
10. VK Klonias, Consistency of two nonparametric maximum penalized likelihood estimators of the probability density function, Ann Statist 10 (1982), 811-824.
11. VK Klonias, On a class of nonparametric density and regression estimators, Ann Statist 12 (1984), 1263-1284.
12. VK Klonias, On the influence function of maximum penalized likelihood density estimators, Nonparametric functional estimation and related topics (G Roussas, ed.), Kluwer, Dordrecht, 1991.
13. HN Mülthei, and B Schorr, On properties of the iterative maximum likelihood reconstruction method, Math Meth Appl Sci 11 (1989), 331-342.
14. MH Protter, and HF Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984.
15. BW Silverman, MC Jones, JD Wilson, and DW Nychka., A smoothed EM algorithm approach to indirect estimation problems, with particular reference to stereology and emission tomography, JR Statist Soc B 52 (1990), 271-324.
16. SL Sobolev, Applications of functional analysis in mathematical physics, American Mathematical Society, Providence, Rhode Island, 1963.
17. RA Tapia, and JR Thompson, Nonparametric density estimation, Johns Hopkins Press, Baltimore, 1979.
18. AN Tikhonov, and VY Arsenin, Solutions of ill-posed problems, John Wiley and Sons, New York, 1977.
19. Y Vardi, LA Shepp, and L Kaufman, A statistical model for positron emission tomography (with discussion), J Amer Statist Assoc 80 (1987), 8-37.