TY  - JOUR
ID  - Szkutnik2007
LB  - Szkutnik2007
AU  - Szkutnik, Zbigniew
TI  - Unfolding spheres size distribution from linear sections with B-splines and EMDS algorithm
ST  - Unfolding spheres size distribution from linear sections with B-splines and EMDS algorithm
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2007
VL  - 27
IS  - 1
SP  - 151
EP  - 165
DO  - http://dx.doi.org/10.7494/OpMath.2007.27.1.151
UR  - http://dx.doi.org/10.7494/OpMath.2007.27.1.151
AB  - The stereological problem of unfolding spheres size distribution from linear sections is formulated as a problem of inverse estimation of a Poisson process intensity function. A singular value expansion of the corresponding integral operator is given. The theory of recently proposed \(B\)-spline sieved quasi-maximum likelihood estimators is modified to make it applicable to the current problem. Strong \(L^2\)-consistency is proved and convergence rates are given. The estimators are implemented with the recently proposed EMDS algorithm. Promising performance of this new methodology in finite samples is illustrated with a numerical example. Data grouping effects are also discussed.
KW  - inverse problem
KW  - singular value expansion
KW  - stereology
KW  - discretization
KW  - quasi-maximum likelihood estimator
SN  - 1232-9274
ER  -