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The purpose of this paper is to construct a key factors selection approach for a class of small-sample multi-factor cross-sectional data analysis (SMCDA) problem, which is very common in productive practice and scientific research, such as coal-bed methane (CBM) content analysis, civil aircraft cost analysis, etc. Key factors selection is an important basic work for SMCDA problem; the proposed method is constructed to improve the accuracy and explanatory of the selected key factors.

Using grey system theory to solve SMCDA problem is more reasonable under few data and poor information. Therefore, this paper constructs a grey incidence analysis (GIA) model with rate of change to select the key factors of an SMCDA problem. The basic idea of the proposed method is to simulate time series by randomly sorting the selected samples, and to calculate the degree of grey incidence with rate of change by loop iterative algorithm, then to construct the degree matrix of grey incidence with rate of change, and finally by which, to utilise quantitative and qualitative analysis methods to select the key factors.

The experimental analysis of application cases demonstrates that the key factors of system’s characteristic can be successfully screened out by the proposed method, the results are consistent with actual conditions, and they have a clearer meaning and a better interpretability.

The method proposed in this paper could be utilised to select key factors for such a class of SMCDA problem, which has fewer observation samples (small-sample), which is influenced by a number of factors (multi-factor) and whose observation samples are placed randomly rather than by time (cross-sectional data). Taking the key influence factors of CBM content and the key driving factors of the vulnerability of agricultural drought in Henan as examples, the results proved the feasibility and superiority of this proposed method.

Most of the existing GIA models mainly focus on these classes of issues with time series data or panel data. However, few GIA models take SMCDA problem as the research object. In this paper, the authors develop the GIA model with rate of change according to the characteristics of SMCDA problem, and present some properties and application suggestions of the proposed method.