Sieve Estimates via Neural Network for Strong Mixing Processes

In this paper, we obtain the convergence rates of sieve estimates for α-mixing strictly stationary processes in the special case of neural networks. When the entropy of sieve satisfies certain conditions, we establish the bounds of sieve estimate. Using the bounds we give finally convergence rate of sieve estimate via neural networks. This revised version was published online in June 2006 with corrections to the Cover Date.