| 部分线性自回归模型中误差方差伪最小二乘估计的渐近正态性 |
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| 引用本文： | 武新乾,田铮,句彦伟. 部分线性自回归模型中误差方差伪最小二乘估计的渐近正态性[J]. 数学季刊, 2006, 21(4): 617-622 |
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| 作者姓名： | 武新乾 田铮 句彦伟 |
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| 作者单位： | Department of Applied Mathematics Northwestern Polytechnical University，Department of Applied Mathematics，Northwestern Polytechnical University，Department of Applied Mathematics，Northwestern Polytechnical University，Xi'an 710072，China，Xi'an 710072，China National Key Laboratory of Pattern Recognition，Beijing 100080，China Institute of Automation，Chinese Academy of Sciences，Beijing 100080，China，Xi'an 710072，China |
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| 摘 要： | Consider the model Y_t=βY_t-1 g(Y_(t-2)) ε_t for 3＜=t＜=T.Here g is an unknown function,βis an unknown parameter,ε_t are i.i.d,random errors with mean 0 and varianceσ~2 and the fourth momentα_4,andε_t are independent of Y_s for all t＞=3 and s=1,2. Pseudo-LS estimators■_T~2,■4T and■_T~2 ofσ~s,α_4 and Var(ε_3~2)are respectively constructed based on piecewise polynomial approximator of g.The weak consistency of■4T and■_T~2 are proved.The asymptotic normality of■_T~2 is given,i.e.T~(1/2)(■_T~2-σ~2)/■_T converges in distribution to N(0,1).The result can be used to establish large sample interval estimates ofσ~2 or to make large sample tests forσ~2.
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| 关 键 词： | 渐近性常态 假LS估计器 误差方差 线性自回归模型 |
Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models |
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| WU Xin-qian,TIAN Zheng,JU Yan-wei. Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(4): 617-622 |
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| Authors: | WU Xin-qian TIAN Zheng JU Yan-wei |
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| Abstract: | |
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| Keywords: | partly linear autoregressive model error variance piecewise polynomial pseudo-LS estimation weak consistency asymptotic normality |
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