误差为鞅差序列的半参数回归模型参数估计的收敛速度

Convergence rate of the parametric estimate of the regression model of half-paramter under error being martingale difference sequence

研究误差为鞅差序列的半参数回归模型参数估计的收敛速度.利用非参数分段多项式估计和最小二乘法进行讨论.考虑固定设计下的半参数回归模型:y_i=x_iβ+g(t_i)+e_i,i=1,2,…,n,{e_i)是随机误差,且{e_i,F_i,i≥1}为平稳遍历的平方可积鞅差序列,F_i,i≥1为单调不减的σ代数流,且Ee^2_1=σ~2>0,E(e^2_i|F_i)≤1,对利用通常采用的非参数权函数法结合最小二乘法得到的参数β和σ~2的估计量(?)_n和(?)~2_n,在适当的条件下得到了(?)_n和(?)~2_n的精确的收敛速度.重对数律.

To study convergence rate of the parametric estimate of the regression model of half-paramter under error being martingale difference sequence. It is discussed by nonparametric piecewise polynomial estimation and least squares estimation. According to the fixed-designed regression model of half-parametric：yi=xiβ＋g（ti）＋ei,i=1,2,……n,（{ei}is the radom error;{ei,Fi,i≥1}is the sequence integrable martingale difference sequence;Fi,i≥1 is the monotone nondecreasing σ- algebraic manifold and Ee^21=σ^2〉0,E（e^2i｜Fi）≤1,with the non-parametric function method and minimum double multiplication, two estimate parameters βn and σn^2 can be concluded. An accurate convergence rate is also provided under some proper condition. Law of iterated logarithm.