On Reconstitution of Smooth Distributions from Grouped Data
Institute for Numerical Mathematics of RAS, Moscow, Russia.
Federal Research Institute for Health Organization and Informatics of the Ministry of Health of the Russian Federation, Moscow, Russia.
Abstract. 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.
Key words: grouped data, smooth distributions, reconstitution, histograms, quadratic programming, nonparametric methods.