摘要
考虑半参数回归模型y_i=X_i~Tβ+g(t_i)+ε_i(i=1,2……,n),其中误差{ε_i,i=1,2……,n}为平稳长程相依(LRD)的随机序列,X_i为随机设计向量.本文用小波估计方法得到参数及非参数的估计量,并在一些适当的条件下研究了它们的弱相合性及弱收敛速度,推广了独立误差半参数回归模型的相应结果.
Abstract
Consider the semiparametric regression model y_i=X_i~Tβ+g(t_i)+ε_i(i= 1,...,n),where random errors{ε_i,i=1,...,n}are stationary and long range dependence (LRD) stochastic processes,and Xi is a vector of random design points.Under this case,the wavelet estimators of both parameters and nonparameters are attained, and consistency and convergence rates in probability are investigated under some mild conditions.Our results generalize some corresponding results in the model with independent random errors.
关键词
半参数回归模型 /
小波估计 /
长相依
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Key words
long range dependence /
semiparametric regression model /
wavelet estimation
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胡宏昌;.
长相依半参数回归模型的小波估计. 数学学报, 2009(04): 19-28 https://doi.org/10.12386/A2009sxxb0080
Hong Chang HU School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,P.R.China.
Wavelet Estimation in Semiparametric Regression Models Under Long Range Dependence. Acta Mathematica Sinica, Chinese Series, 2009(04): 19-28 https://doi.org/10.12386/A2009sxxb0080
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脚注
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