On the properties of small sample of GM(1,1) model

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In grey prediction modeling, the more samples selected the more errors. This paper puts forward new explanations of "incomplete information and small sample" of grey systems and expands the suitable range of grey system theory. Based on the geometric sequence, it probes into the influence on the relative errors by selecting the different sample sizes. The research results indicate that to the non-negative increasing monotonous exponential sequence, the more samples selected, the more average relative errors. To the non-negative decreasing monotonous exponential sequence, a proper sample number exists that has the least average relative error. When the initial value of the sequence of raw data of new information GM(1,1) model changes, the development coefficient remains unchanged. The segmental correction new information GM(1,1) model (SNGM) can obviously improve the simulation accuracy. It puts forward the mathematic proofs that the small sample usually has more accuracy than the large sample when establishing GM(1,1) model in theory. © 2008 Elsevier Inc. All rights reserved.

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Yao, T., Liu, S., & Xie, N. (2009). On the properties of small sample of GM(1,1) model. Applied Mathematical Modelling, 33(4), 1894–1903. https://doi.org/10.1016/j.apm.2008.03.017

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