Indeks kulturne politike za države EU: uporaba multivariatne analize v visoko-dimenzionalnih okoljih

The new era of statistics has been described as the »age of big data« (Hellerstein 2008). Although describing a different problem, problems of high-dimensional data have also been ever more frequently present in statistical and econometric literature in past years (see e.g. Bai 2003; Bai & Ng 2003; Chernozhukov & Hansen 2013; Belloni, Chernozhukov & Hansen 2011; Koch 2013), describing statistical analysis in the presence of much higher number of variables than observations. In our article, we will analyze the problems of high-dimensionality when constructing indexes for a selected array of data. Such problems frequently abound with using macroeconomic data when data exist for a selected group (usually a smaller number) of countries and one wants to estimate a composite measure (index) for benchmarking and statistical comparison. Tools from multivariate analysis (factor analysis, principal components, clustering, multidimensional scaling) can be fruitfully used to this purpose, as well as shrinkage and penalized regressions (see e.g. Fan & Lv 2008; Fan & Lv 2010; Fan et al. 2010).

In the first part of the article we will therefore present the problem in a general statistical framework, showing that high-dimensionality of data can significantly alter the construction of an index, particularly in sparse environments. We will present some new statistical results and solutions for robustness of the constructed index. In the second part we will apply the findings to construction of a »cultural policy index«, based on data for over 400 variables for 35 European countries from Eurostat's Cultural Statistics 2007 and 2011 Pocketbooks and Compendium for Cultural Policies and Trends in Europe. As cultural statistics is characterized by problems of unclear classification and missing data, imputation methods have to be used, as well as high-dimensional multivariate and regression analysis (see e.g. Koch 2013). The results will enable us to present a new measure in the field of cultural policy and cultural statistics to estimate the performance of cultural policy of a country (at present almost no such tools based on solid statistical analysis exist). Generalizations to indexes in other sectors in the economy and the public sector will also be made.


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