﻿ 基于面板数据的灰色曲率关联模型
 控制与决策  2020, Vol. 35 Issue (5): 1072-1076 0

### 引用本文 [复制中英文]

[复制中文]
WU Hong-hua, QU Zhong-feng. The grey curvature incidence model based on panel data[J]. Control and Decision, 2020, 35(5): 1072-1076. DOI: 10.13195/j.kzyjc.2019.0441.
[复制英文]

### 文章历史

The grey curvature incidence model based on panel data
WU Hong-hua , QU Zhong-feng
School of Mathematical Sciences, University of Jinan, Jinan 250022, China
Abstract: The panel data is projected to the time dimension discrete curves and the index dimension discrete curves. Then, based on the thinking of discrete curvature, the incidence coefficient formulas of the time dimension and index dimension are respectively constructed. The grey curvature incidence model is constructed. The properties of the model, e.g., normalization, symmetry, similarity and translation invariance, are also satisfied. Finally, the comparison to some existing models and an example are given to illustrate the rationality of the proposed model, and the results show that the proposed model can better reflect incidence degree of panel data.
Keywords: degree of incidence    grey system    curvature    panel data    discrete curve
0 引言

1 相关知识

Xis称为面板数据Xi关于指标s的时间维度离散曲线.

(xi(s, t))t'、(xi(s, t))s'分别称为样本Xi在点(s, t)处关于时间和指标的一阶差分. (xi(s, t))tt"、(xi(s, t))ss''分别称为样本Xi在点(s, t)处关于时间和指标的二阶差分.

|Kis(t)|值越大, 表明曲线在时间维度的弯曲程度越大, 反之越小.若Kis(t)>0, 则曲线的弯曲方向向上; 若Kis(t) < 0, 则曲线的弯曲方向向下; 若Kis(t)=0, 则曲线退化为直线.

1) 如果数据为成本型, 则有

2) 如果数据为效益型, 则有

3) 如果数据为居中型, 则有

2 灰色曲率关联度

ρij(s, t)称为样本XiXj在点(s, t)关于时间维度关联系数.

σij(s, t)称为样本XiXj在点(s, t)关于指标维度关联系数.

ρij称为样本XiXj的时间维度关联度.

σij称为样本XiXj的指标维度关联度.

ρij(s, t)≤ 1, 则有ρij≤1.同理, 对于指标维度关联度, σij≤1, 所以0 < αρij+βσij≤1(α>0, β>0, α+β=1), 满足规范性公理.

2) 接近性.由两面板数据在点(s, t)处关于时间维度和指标维度关联系数公式可以得到, 当他们关于时间维度和指标维度的离散曲率越接近, 相应的关联系数越大, 从而灰色曲率关联度越大, 满足接近性公理.

3 比较分析

 图 1 各组面板数据的三维曲线

4 实例分析

5 结论

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