Apibendrintų Gini indeksų taikymas reitingavimo modeliams

LTStraipsnyje nagrinėjama apibendrintų Gini indeksų taikymo sudarant įmonių reitingavimo modelius galimybė. Pasitelkus tipinės Lorenz kreivės ir Gini indekso sąvokas, apibrėžiamas Gini indeksas, taikytinas reitingavimo modeliui atrenkant finansinius ir nefinansinius rodiklius, leidžiančius kuo tiksliau atskirti mokias įmones nuo galinčių tapti nemokiomis. Remiantis G. A. Koshevoy ir K. Mosler plėtotomis daugiamačio Gini indekso idėjomis, pristatomi du apibendrinti reitingavimo modelių Gini indeksai - normos ir tūrio. Straipsnyje nenurodoma, kurį Gini indeksą - vienmatį, normos ar tūrio - labiausiai tinka taikyti finansinių ir nefinansinių rodiklių atrankai, tačiau pateikiami siūlymai, kaip tai nustatyti. [Iš leidinio]Reikšminiai žodžiai: Gini indeksas; Lorenz kreivė; Reitingavimo modelis; Gini indexes; Lorenz curve; Rating model; Zonoidas; Gini Index; Zonoid; Scoring model.

ENThe main purpose of this paper is to build the generalized Gini index of scoring model following the theory of zonoids. In the first part of the paper the usual Lorenz curve, traditional Gini index and its summary measures are presented. The second part presents the definition of the scoring models Gini index according to scoring model power measures applied in BIS resolutions. Furthermore Gini indexes of Lorenz curve bottom and top approximations are defined and two its summary measures - norm and volume Gini indexes are derived. Norm Gini index is constructed replacing the single financial factor indicator with the norm of d financial factors indicators vector in the formula of scoring models Gini index. As far as the theory of zonoids can not be followed directly to define k-dimensional scoring models Gini index ideas of this theory are applied to the definition of Lorenz surface top and bottom approximations and volume Gini index is constructed. Finally the stability of univariate, norm and volume Gini indexes is analysed using Jacknife variance estimations. The analysis on the available data sample showed that the value of Gini indexes Jacknife variance estimates is rather small therefore both one-dimensional and k-dimensional Gini indexes are considered stable. However general conclusion on the decision which Gini index - one-dimensional, norm or volume - to use for financial factors selection to the scoring model can not be made. Considering particular data sets, separate analysis on Gini index stability should be performed applying Jacknife or bootstrap methods. [From the publication]