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《Chinese Journal of Applied Probability and Statistics》 2010-01
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Convergence Rate of Wavelet Estimator in Semiparametric Models with Dependent MA(∞) Error Process

Liang Hanying Wang Xiaozhi(Department of Mathematics,Tongji University,Shanghai,200092)  
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.
【Fund】: supported by the National Natural Science Foundation of China(10871146)
【CateGory Index】: O212.1
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