纳税评估的广义回归神经网络建模与实证

General Regression Neural Network Based on Tax Payment Assessment and Its Empirical Research

针对上海市某区386家中小企业15个财务指标数据,运用灵敏度分析方法筛选出对判定纳税情况具有显著影响的10个评价指标,采用自组织神经网络方法把全部386个样本分成性质相似的训练样本、检验样本和测试样本,通过逐步减小光滑因子值确定其合理值,建立纳税评估广义回归神经网络(GRNN)模型。与线性回归、判别分析、Logistic和支持向量机等模型的结果对比表明:GRNN模型的分类错误率最低,检验样本和测试样本的II类和I类分类错误率分别低于5.4%和2.0%,平均分类错误率低于2.5%.对另外339家企业纳税情况的判定结果表明,建立的GRNN模型具有很好的泛化能力和鲁棒性。

Based on the 15 indexes＇ （or variables＇） financial data of 386 small- and medium-sized enterprises （SMEs） located in some district of Shanghai city, the ten variables mainly influencing the tax situation （tax evasion or compliance） of the 386 SMEs are obtained by applying sensitivity analysis method for selecting input variahles. The training set data, verification set data （taking up 24.4%0 ） and testing set data （taking up 21.0% ） with similar and high quality characteristics --similar mean values and variance--are divided using self-organizing map （SOM） approach. The holdout method is used to determine the reasonable value smoothness a for which the root-mean-squared error （RMSE） of the verification set data and testing set data is the minimum. The feasible and effective GRNN model for tax payment assessment is thus established in this paper. Compared with the multivariate linear regression, logistic, the multivariate discriminant analysis and the support vector machine, the general regression neural network （GRNN） model established in this paper possesses the most accurate, and the classification-error percentage （CEP） is the lowest in the five models. The Type I CEP of verification set data and testing set data is lower than 2.00% and the Type II CEP lower than 5.4 %, the average CEP is lower than 2.5 %. The two- and three- dimensional relations between the indexes and the tax situation （i. e. GRNN output） are respectively studied and plotted. The tax payment situation of the other 339 SMEs is also assessed and judged, and the results show that the established GRNN model possesses high generalization and robustness.