相依MA(∞)误差下半参数模型小波估计的收敛速度(英文)

Convergence Rate of Wavelet Estimator in Semiparametric Models with Dependent MA(∞) Error Process

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.

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=^∞∑j=-∞ cjei-j with ^∞∑j=-∞｜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.