????MA($\infty$)????°???????С??????????????

考虑半参数回归模型$y_i=x_i\beta+g(t_i)+V_i$ $(1\le i\len)$, 其中$(x_i,t_i)$是已知的设计点, 斜率参数$\beta$是未知的,$g(\cdot)$是未知函数, 误差$V_i=\tsm^\infty_{j=-\infty}c_je_{i-j}$,$\tsm^\infty_{j=-\infty}|c_j|<\infty$并且$e_i$是负相关的随机变量.在适当的条件下, 我们研究了$\beta$与$g(\cdot)$小波估计量的强收敛速度.结果显示$g(\cdot)$的小波估计量达到最优收敛速度. 同时,对$\beta$小波估计量也作了模拟研究.

Convergence Rate of Wavelet Estimator in SemiparametricModels with Dependent MA($\infty$) Error Process

Consider semiparametric regression model$y_i=x_i\beta+g(t_i)+V_i$ ($1\le i\le n)$, where the known designpoints $(x_i,t_i)$, the unknown slope parameter $\beta$, and thenonparametric component $g$ are non-random, and the correlatederrors $V_i=\tsm^\infty_{j=-\infty}c_je_{i-j}$ with$\tsm^\infty_{j=-\infty}|c_j|<\infty$ and $e_i$ are negativelyassociated random variables. Under appropriate conditions, we studyrates of strong convergence for wavelet estimators of $\beta$ and$g(\cdot)$. The results show that the wavelet estimator of$g(\cdot)$ can attain the optimal convergence rate. Finite samplebehavior of the estimator of $\beta$ is investigated via simulationstoo.