基于G-Q的K-S异方差检验方法
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摘要
在异方差线性回归模型中,G-Q检验是常用的方法,但G-Q检验通常适用于一元线性回归模型中,且有适用条件;而在多元线性回归模型中,G-Q检验也不是一个有效的异方差检验方法。针对G-Q检验的局限性,文章基于G-Q检验的基本思想,采用非参数Kolmogorov-Smirnov检验对线性回归模型进行异方差检验。通过大量数值模拟和实证分析,结果表明该方法具有一定的可行性和可靠性。
In the heteroskedastic linear regression model,G-Q test is a commonly used method.However,the G-Q test is mostly applied to the one-dimensional linear regression model and has certain limited conditions,and in the multiple linear regression model,the G-Q test is not a valid method to conduct heteroscedasticity test.For the limitation of G-Q test,based on the idea of G-Q test,Kolmogorov-Smirnov test,a non-parametric test method,was used to test the heteroskedasticity of the linear regression model.Based on the lots of numerical simulation and empirical analysis,the results show that this method has certain feasibility and reliability.
In the heteroskedastic linear regression model,G-Q test is a commonly used method.However,the G-Q test is mostly applied to the one-dimensional linear regression model and has certain limited conditions,and in the multiple linear regression model,the G-Q test is not a valid method to conduct heteroscedasticity test.For the limitation of G-Q test,based on the idea of G-Q test,Kolmogorov-Smirnov test,a non-parametric test method,was used to test the heteroskedasticity of the linear regression model.Based on the lots of numerical simulation and empirical analysis,the results show that this method has certain feasibility and reliability.
引文
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[18] Hesamian G,Chachi J.Two-sample Kolmogorov-Smirnov Fuzzy Test for Fuzzy Random Variables[J].Statistical Papers,2015,56(1):61-82.DOI:10.1007/s00362-013-0566-2.
[19] Xiao Y.A Fast Algorithm for Two-dimensional Kolmogorov-Smirnov Two Sample Tests[J].Computational Statistics&Data Analysis,2017,105(C):53-58.DOI:10.1016/j.csda.2016.07.014.
[20]夏帆,倪青山.基于分布拟合的异方差检验[J].数量经济技术经济研究,2012(8):114-123.DOI:10.13653/j.cnki.jqte.2012.08.011.Xia F,Ni Q S.A Test for Heteroscedasticity Based on the Goodness-of-fit Test[J].The Journal of Quantitative&Technical Economic,2012(8):114-123.DOI:10.13653/j.cnki.jqte.2012.08.011.
[21]陈强.高级计量经济学及Stata应用[M].北京:高等教育出版社,2014.
[22]中华人民共和国国家统计局中国统计年鉴[M].北京:中国统计出版社,2014.
[2]白雪梅.异方差性的检验方法及评述[J].东北财经大学学报,2002(6):26-29.DOI:10.19653/j.cnki.dbcjdxxb.2002.06.002.Bai X M.Testing Methods and Comments based on Heteroscedasticity[J].Journal of Dongbei Unirersity of Finance and Economics,2002(6):26-29.DOI:10.19653/j.cnki.dbcjdxxb.2002.06.002.
[3] Glejser H.A New Test for Heteroskedasticity[J].Publications of the American Statistical Association,1969,64(325):316-323.DOI:10.2307/2283741.
[4] Goldfeld S,Quandt R.Some Tests for Homoscedasticity[J].Publications of the American Statistical Association,1965,60(310):539-547.DOI:10.2307/2282689.
[5]White H.A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity[J].Econometrica,1980,48(4):817-838.DOI:10.2307/1912934.
[6] Park R E.Estimation with Heteroscedastic Error Terms[J].Econometrica,1966,34(4):888-888.DOI:10.2307/1910108.
[7] Breusch T S,Pagan A R.A Simple Test for Heteroscedasticity and Random Coefficient Variation[J].Econometrica,1979,47(5):1287-1294.DOI:10.2307/1911963.
[8] Godfrey L G.Testing for Multiplicative Heteroskedasticity[J].Journal of Econometrics,1978,8(2):227-236.DOI:10.1016/0304-4076(78)90031-3.
[9] Engle R F.Autoregressive Conditional Heteroscedasticty with Estimates of the Variance of United Kingdom Inflation[J].Econometrica,1982,50(4):987-1007.DOI:10.2307/1912773.
[10] Cribari-Neto F,Souza T C,Vasconcellos K L P.Inference Under Heteroskedasticity and Leveraged Data[J].Communications in Statistics,2007,36(10):18771888.DOI:10.1080/03610920601126589.
[11]张晓琴,王佳鸣.基于正交表的异方差估计方法改进[J].数理统计与管理,2016,35(2):225-231.DOI:10.13860/j.cnki.sltj.20160322-021.Zhang Xiaoqin,Wang Jiaming.An Improvement Estimation Method of the Variance with Orthogonal Table in the Heteroskedastic Model[J].Journal of Applied Statistics and Management,2016,35(2):225-231.DOI:10.13860/j.cnki.sltj.20160322-021.
[12]李顺勇,张娜慧,张晓琴.基于成分数据的异方差模型[J].山西大学学报(自然科学版),2016,39(4):549-555.DOI:10.13451/j.cnki.shanxi.univ(nat.sci.).2016.04.001.Li S Y,Zhang N H,Zhang X Q.Heteroskedastic Model Based on Compositional Data[J].Journal of Shanxi University(Natural Science Edition),2016,39(4):549-555.DOI:10.13451/j.cnki.shanxi.univ(nat.sci.).2016.04.001.
[13]李顺勇,钱宇华,张晓琴,等.基于变量选择和聚类分析的两阶段异方差模型估计[J].应用概率统计,2018,34(2):191-200.DOI:10.3969/j.issn.1001-4268.2018.02.007.Li S Y,Qian Y H,Zhang X Q,et al.Two-Stage Estimation about Heteroscedastic Model Based on Variable Selection and Cluster Analysis[J].Chinese Journal of Applied Probability and Statistics,2018,34(2):191-200.DOI:10.3969/j.issn.1001-4268.2018.02.007.
[14] Sevil Y C,Yildiz T O.Power Comparison of the Kolmogorov-Smirnov Test under Ranked Set Sampling and Simple Random Sampling[J].Journal of Statistical Computation&Simulation,2017:1-11. DOI:10.1080/00949655.2017.1319948.
[15] Al-Labadi L,Zarepour M.Two-sample Kolmogorov-Smirnov Test Using a Bayesian Nonparametric Approach[J].Mathematical Methods of Statistics,2017,26(3):212-225.DOI:10.3103/S1066530717030048.
[16] Frey J.An exact Kolmogorov-Smirnov Test for Whether Two Finite Populations Are the Same[J].Statistics&Probability Letters,2016,116:65-71.DOI:10.1016/j.spl.2016.04.016.
[17] Hassani H,Silva E S.A Kolmogorov-Smirnov Based Test for Comparing the Predictive Accuracy of Two Sets of Forecasts[J].Econometrics,2015,3(3):590-609.DOI:10.3390/econometrics3030590.
[18] Hesamian G,Chachi J.Two-sample Kolmogorov-Smirnov Fuzzy Test for Fuzzy Random Variables[J].Statistical Papers,2015,56(1):61-82.DOI:10.1007/s00362-013-0566-2.
[19] Xiao Y.A Fast Algorithm for Two-dimensional Kolmogorov-Smirnov Two Sample Tests[J].Computational Statistics&Data Analysis,2017,105(C):53-58.DOI:10.1016/j.csda.2016.07.014.
[20]夏帆,倪青山.基于分布拟合的异方差检验[J].数量经济技术经济研究,2012(8):114-123.DOI:10.13653/j.cnki.jqte.2012.08.011.Xia F,Ni Q S.A Test for Heteroscedasticity Based on the Goodness-of-fit Test[J].The Journal of Quantitative&Technical Economic,2012(8):114-123.DOI:10.13653/j.cnki.jqte.2012.08.011.
[21]陈强.高级计量经济学及Stata应用[M].北京:高等教育出版社,2014.
[22]中华人民共和国国家统计局中国统计年鉴[M].北京:中国统计出版社,2014.