鞅差误差下部分线性变系数模型误差方差的Jackknife经验似然
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摘要
研究了鞅差误差下部分线性变系数模型误差方差的Jackknife经验似然.首先得到了误差方差的Jackknife估计量,其次利用所得到的估计量构造了误差方差的Jackknife经验似然统计量,进一步证明了所提出的估计量渐近服从正态分布,Jackknife经验似然统计量渐近服从卡方分布.
This paper studies the Jackknife empirical likelihood of error variance in partial linear varyingcoefficient model under martingale difference.First,the Jackknife estimator of the error variance was obtained,and then the Jackknife empirical likelihood statistic of the error variance was constructed by using the Jackknife estimator obtained.It was proved that the proposed estimator asymptotically obeys the normal distribution and the Jackknife empirical likelihood statistic asymptotically follows the chi-square distribution.
This paper studies the Jackknife empirical likelihood of error variance in partial linear varyingcoefficient model under martingale difference.First,the Jackknife estimator of the error variance was obtained,and then the Jackknife empirical likelihood statistic of the error variance was constructed by using the Jackknife estimator obtained.It was proved that the proposed estimator asymptotically obeys the normal distribution and the Jackknife empirical likelihood statistic asymptotically follows the chi-square distribution.
引文
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[11]杨善朝.鞅差序列下回归函数加权核估计[J].数理统计与应用概率论,1998,13(1):17-22.
[12]万成高.鞅的极限理论[M].北京:科学出版社,2002.
[13]A B Owen.Empirical Likelihood Ratio Confidence Regions[J].Ann.Stat.,1990,18(1):90-120.
[2]I Ahmad,S Leehalanon,Q Li.Efficient Estimation of a Semiparametric Partially Linear Varying-coefficient Model[J].Ann.Stat.,2005,33(1):258-283.
[3]J You,Y Zhou.Empirical Likelihood for Semiparametric Varying-coefficient Partially Linear Regression Models[J].Stat.Probab.Lett.,2006,76(4):412-422.
[4]Z Huang,R Zhang.Empirical Likelihood for Nonparametric Parts in Semiparametric Varying-coefficient Partially Linear Models[J].Stat.Probab.Lett.,2009,79(16):1 798-1 808.
[5]X Wang,G Li,L Lin.Empirical Likelihood Inference for Semiparametric Varying-coefficient Partially Linear EV Models[J].Metrika,2011,73(2):171-185.
[6]F Bravo.Varying Coefficients Partially Linear Models with Randomly Censored Data[J].Ann.Inst.Stat.Math.,2014,66(2):383-412.
[7]M H Quenouille.Approximate Test of Time Series[J].J.R.Statist.Soc.B,1949,11(1):68-84.
[8]J M Tukey.Preliminary Report[J].Ann.Math.Stat.,1958,29(2):614.
[9]B Y Jing,Z Wang.Jackknife Empirical Likelihood[J].J.Amer.Statist.Assoc,2009,104(487):1 224-1 232.
[10]H Y Liang,A A Liu.Jackknife Empirical Likelihood of the Error Variance in Partially Linear Varying-coefficient Errors-in-variables Models[J].Statist.Papers,2017,58(1):95-122.
[11]杨善朝.鞅差序列下回归函数加权核估计[J].数理统计与应用概率论,1998,13(1):17-22.
[12]万成高.鞅的极限理论[M].北京:科学出版社,2002.
[13]A B Owen.Empirical Likelihood Ratio Confidence Regions[J].Ann.Stat.,1990,18(1):90-120.