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

Tatyana V. Zhgun; Tatyana V. Zhgun

doi:10.3934/NAR.2019.1.42

National Accounting Review

2019, Volume 1, Issue 1: 42-61. doi: 10.3934/NAR.2019.1.42

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Research article

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

Tatyana V. Zhgun ^,

Department of Applied Mathematics and Computer Science, Novgorod State University, Velikiy Novgorod, Russia

Received: 29 December 2019 Accepted: 26 February 2019 Published: 20 August 2019
JEL Codes: C38, I38, O15, R13

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.
Citation: Tatyana V. Zhgun. Constructing a stable complex index of a system's quality for a series of observations[J]. National Accounting Review, 2019, 1(1): 42-61. doi: 10.3934/NAR.2019.1.42

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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.

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