鞅差时间序列的部分线性EV模型的小波估计
|
摘要
用小波方法研究了误差为滑动平均鞅差序列的部分线性EV模型,得到了小波估计量的矩收敛速度及强收敛性。
Using wavelet method,we consider a partly linear EV model with moving average errors generated by a martingale difference sequence. We investigate the moment convergence rates and strong consistency of wavelet estimators.
Using wavelet method,we consider a partly linear EV model with moving average errors generated by a martingale difference sequence. We investigate the moment convergence rates and strong consistency of wavelet estimators.
引文
[1]Hu shuhe.Fixed-design semiparametric regression for linear time series[J].Acta Mathematica Scientia,2006,26B(1):74~82.
[2]胡宏昌,胡迪鹤.鞅差时间序列半参数回归模型的小波估计[J].数学进展,2010,39(1):23~30.
[3]Lanh Tran,George Roussas,Sidney Yakowitz,et al.Fixed-design regression for linear time series[J].The Annals of Statistics,1996,24(3):975~991.
[4]An H Z,Chen Z G,Hannan J E.Autoccorrelation,autoregression and autoregressive approximation[J].Theannals of Statistics,1982,10:926~936.
[5]Jan Beran.Statistics for long-memory processes[M].New York:Chapiman&Hall,1994.
[6]Donatas Surgailils,Marius Vaiciulis.Convergence of appell polynomials of long range dependent moving averages in martingale differences[J].Acta Applicandae Mathematicae,1999,58:343~357.
[7]Liang H,Hardle W,Carroll R J.Estimation in a semiparametric partially linear errors-in-variables model[J].The Annals of Statistics,1999,27:1519~1535.
[8]Antoniads A,Gregorie G,Mckeague I W.Wavelet methods for curve estimation[J].Journal of the American Statistical Association,1994,89:1340~1353.
[9]Hu H C.Ridge estimation of a semiparametric regression model[J].Journal Computational and Applied Mathematics,2005,176:215~222.
[10]Zhou X,You J H.Wavelet estimation in varying-coefficient partially linear regression models[J].Statistics&Probability Letters,2004,68:91~104.
[11]钱伟民,柴根象.半参数回归模型小波估计的强逼近[J].中国科学(A辑),1999,29(3):233~240.
[12]胡宏昌,胡迪鹤.半参数回归模型小波估计的强相合性[J].数学学报,2006,49(6):1417~1424.
[13]Hu H C.Convergence rates of wavelet estimators in semiparametric regression models with martingale difference error[J].Journal of Mathematical Sciences:Advances and Applications,2009,3:4~19.
[2]胡宏昌,胡迪鹤.鞅差时间序列半参数回归模型的小波估计[J].数学进展,2010,39(1):23~30.
[3]Lanh Tran,George Roussas,Sidney Yakowitz,et al.Fixed-design regression for linear time series[J].The Annals of Statistics,1996,24(3):975~991.
[4]An H Z,Chen Z G,Hannan J E.Autoccorrelation,autoregression and autoregressive approximation[J].Theannals of Statistics,1982,10:926~936.
[5]Jan Beran.Statistics for long-memory processes[M].New York:Chapiman&Hall,1994.
[6]Donatas Surgailils,Marius Vaiciulis.Convergence of appell polynomials of long range dependent moving averages in martingale differences[J].Acta Applicandae Mathematicae,1999,58:343~357.
[7]Liang H,Hardle W,Carroll R J.Estimation in a semiparametric partially linear errors-in-variables model[J].The Annals of Statistics,1999,27:1519~1535.
[8]Antoniads A,Gregorie G,Mckeague I W.Wavelet methods for curve estimation[J].Journal of the American Statistical Association,1994,89:1340~1353.
[9]Hu H C.Ridge estimation of a semiparametric regression model[J].Journal Computational and Applied Mathematics,2005,176:215~222.
[10]Zhou X,You J H.Wavelet estimation in varying-coefficient partially linear regression models[J].Statistics&Probability Letters,2004,68:91~104.
[11]钱伟民,柴根象.半参数回归模型小波估计的强逼近[J].中国科学(A辑),1999,29(3):233~240.
[12]胡宏昌,胡迪鹤.半参数回归模型小波估计的强相合性[J].数学学报,2006,49(6):1417~1424.
[13]Hu H C.Convergence rates of wavelet estimators in semiparametric regression models with martingale difference error[J].Journal of Mathematical Sciences:Advances and Applications,2009,3:4~19.