部分线性自回归模型中误差矩的分段多项式估计

Piecewise polynomial estimates of error moments inpartly linear autoregressive models

目的研究部分线性自回归模型中误差矩的估计。方法利用非参数分段多项式估计和最小二乘法进行讨论。结果给出了误差tε的k(k≥1)阶矩及误差方差σ2的估计的大样本性质。结论误差k(k≥1)阶矩的估计的收敛速度为T-1/2,T(^σ2T-σ2)/D^T依分布收敛于N(0,1),其中^σ2T和D^2T分别为σ2和Var(23ε)的分段多项式估计,T为数据个数。

Aim To study discussed by nonparametric properties for the estimators the estimates of error moments in partly linear autoregressive models. Methods It is piecewise polynomial estimation and least squares estimation. Results Large sample of k-th （ k ≥ 1 ） order moment of the error ε, and the error variance o-2 are given. Conclusion The rate of convergence of the estimator of k-th （ k I〉 1 ） order moment of the error is T^-1/2 and √T（ δ^2T - σ2 ）/DT converges in distribution to N（0,1 ）. Here δ^2T and D^2T are piecewise polynomial estimators of o＂2 and Var （ ε^23 ） respectively and T is the number of data.