Constructing a stable complex index of a system’s quality for a series of observations

Abstract

This paper discusses the solution to the problem of constructing latent complex indexes of a change in a system’s quality for several observations in the absence of training. An analysis of the stability of such a solution is also provided. The algorithm for constructing complex indexes is implemented with the definition of non-random variables of the principal component characterizing the structure of the system under discussion. The algorithm uses a new approach to choose the principal component number, determine the weights of the considered variables and subsystems, and to determine the information content of the complex index based on the selected signal-to-noise ratio parameter. The algorithm was used to obtain complex indexes of quality of life for Russia’s constituent entities for 2007–2016. The analysis of the obtained solution’s quality shows its high resistance to changes in the input data.

Keywords

• composite index
• data error
• principal component analysis
• signal-to-noise ratio
• signal detection in noise
• informativeness of the principal component analysis
• stability of composite index
• rank robustness tests