Vladimir NORKIN’s research

Research directions:

• Nonconvex stochastic programming
• Stochastic integer and global optimization
• Nonsmooth / nondifferentiable optimization
• Probabilistic & Statistical aspects of SP
• Risk & Insurance
• Mathematical economics
• Nonparametric data analysis
• Summary of results

Nonparametric Data Analysis

In Norkin (2003, 1990) to discover and identify a (linear) dependence in experimental data, a principal component method in its geometric form is applied: data are approximated by a linear manifold formed by some first principal components of a data space. If the dimension of the manifold is less than a dimension of the space, then a linear dependence in data is identified. Problems of selection of dependent, independent and neutral variables and problem of multicollinearity of observations are resolved in a natural way in this approach.

In Kirilyuk, Norkin and Domrachev (2000-2002) an approach of nonparametric indexes (data envelope analysis) is applied to actors of Ukrainian financial and agricultural markets to estimate their position relative to market efficiency frontier.

Selected references

Norkin V.I. (2003). On application of principle components method in multi-dimensional regression analysis, Komputernaya matematika (Computer mathematics), Institute of Cybernetics, Kiev, 2003, N 2, 29-36 (In Russian).

Norkin V.I. (1990). Construction of linear models on the basis of limited experimental data, in: Mathematical Methods of Decision-Making under uncertainty, Eds. Yu.M.Ermoliev and I.N.Kovalenko, Glushkov Institute of Cybernetics, Kiev, 1990, 77-82 (In Russian).

Kirilyuk V.S., Norkin V.I. and Domrachev V.N. (2002). A nonparametric index approach for the evaluation of financial market actors through return-risk trade-off on example of commercial banks, Problemy upravleniya i informatiki (In Russian, English translation in J. of Automation and Information Sciences), 2002, ¹ 6, 120-131.

Kirilyuk V.S., Norkin V.I. and Domrachev V.N. (2002). On the use of a return-risk frontier for the evaluation of banks functioning, Finansovye riski (Financial risks), 2002, No. 1-2(29), pp.75-77. (In Russian).

Kirilyuk V.S., Norkin V.I. and Domrachev V.N. (2001).Method of nonparametric indexes for the analysis of productivity, technical growth and efficiency chainge on the example of Ukrainian agriculture in 1996-1999, Finansovye riski (Financial risks), 2001, No. 3(27), pp.77-84. (In Russian).