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 design points (x_i,t_i), the unknown slope parameter \beta, and the nonparametric component g are non-random, and the correlated errors V_i=\tsm^\infty_j=-\inftyc_je_i-j with \tsm^\infty_j=-\infty|c_j|<\infty and e_i are negatively associated random variables. Under appropriate conditions, we study rates 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 sample behavior of the estimator of \beta is investigated via simulations too.