Geodesic
On reconstitution of smooth distributions from grouped data
Matematičeskaâ biologiâ i bioinformatika, Tome 11 (2016) no. 2, pp. 367-384.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, proposed is a simple nonparametric method of reconstitution of smooth distributions of additive quantities from grouped data. The method is based on the requirement of minimization of the norm of non-smoothness measure of the solution under the condition of exact equality of the group sums, which reduces the problem to the quadratic programming problem. The method was tested on the age-at-death data; its precision was shown to be comparable to and exceeding the precision of a method of other authors. After testing it on the cancer incidence data, some drawbacks and limitations of the nonparametric approach were determined. The advantages of the proposed method are algorithmic and computational simplicity, good flexibility of the mathematical model. 
@article{MBB_2016_11_2_a20,
     author = {K. K. Avilov},
     title = {On reconstitution of smooth distributions from grouped data},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {367--384},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2016_11_2_a20/}
}
TY  - JOUR
AU  - K. K. Avilov
TI  - On reconstitution of smooth distributions from grouped data
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2016
SP  - 367
EP  - 384
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2016_11_2_a20/
LA  - ru
ID  - MBB_2016_11_2_a20
ER  - 
%0 Journal Article
%A K. K. Avilov
%T On reconstitution of smooth distributions from grouped data
%J Matematičeskaâ biologiâ i bioinformatika
%D 2016
%P 367-384
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2016_11_2_a20/
%G ru
%F MBB_2016_11_2_a20
K. K. Avilov. On reconstitution of smooth distributions from grouped data. Matematičeskaâ biologiâ i bioinformatika, Tome 11 (2016) no. 2, pp. 367-384. http://geodesic.mathdoc.fr/item/MBB_2016_11_2_a20/

[1] Rizzi S., Gampe J., Eilers P. H. C., “Efficient Estimation of Smooth Distributions From Coarsely Grouped Data”, American Journal of Epidemiology, 182:2 (2015), 138–147 | DOI

[2] Underlying cause of death 1999–2010 on CDC WONDER Online Database, , National Center for Health Statistics, Centers for Disease Control and Prevention (accessed 06 November 2016) http://wonder.cdc.gov/ucd-icd10.html

[3] R Core Team. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2013

[4] Kuhn H. W., Tucker A. W., “Nonlinear programming”, Proceedings of 2nd Berkeley Symposium, University of California Press, Berkeley, 1951, 481–492 | MR

[5] Karush W., Minima of Functions of Several Variables with Inequalities as Side Constraints, Chicago, Illinois, 1939 | MR

[6] Nocedal J., Wright S. J., Numerical Optimization, 2nd ed., Springer-Verlag, Berlin–New York, 2006 | MR | Zbl

[7] Gould N., Toint P. L., “Preprocessing for quadratic programming”, Math. Programming, Series B, 100 (2004), 95–132 | MR | Zbl

[8] Chislennost postoyannogo naseleniya-zhenschin po vozrastu na 1 yanvarya, , Edinaya mezhvedomstvennaya informatsionno-statisticheskaya sistema (EMISS) (data obrascheniya 11.11.2016) https://fedstat.ru/indicator/33459

[9] A. D. Kaprin, V. V. Starinskii, G. V. Petrova (red.), Zlokachestvennye novoobrazovaniya v Rossii v 2014 godu (zabolevaemost i smertnost), MNIOI im. P.A. Gertsena - filial FGBU «NMIRTs» Minzdrava Rossii, M., 2016