【摘要】 考虑半参数回归模型yi=xiβ+g(ti)+Vi(1≤i≤n), 其中(xi,ti)是已知的设计点, 斜率参数β是未知的, g(·)是未知函数, 误差Vi=sum from j=-∞ to ∞(cjei-j),sum from j=-∞ to ∞(|cj|<∞)并且ei是负相关的随机变量. 在适当的条件下, 我们研究了β与g(·)小波估计量的强收敛速度. 结果显示g(·)的小波估计量达到最优收敛速度. 同时, 对β小波估计量也作了模拟研究.更多还原

【Abstract】 Consider semiparametric regression model yi=xiβ+g(ti)+Vi(1≤i≤n),where the known design points(xi,ti),the unknown slope parameter β,and the nonparametric component g are non-random,and the correlated errors Vi=sum from j=-∞ to ∞(cjei-j) with sum from j=-∞ to ∞(|cj|<∞) and ei are negatively associated random variables.Under appropriate conditions,we study rates of strong convergence for wavelet estimators of β and g(·).The results show that the wavelet estimator of g(·) can attain the optimal convergence rate.Finite sample behavior of the estimator of β is investigated via simulations too.更多还原