Root-n-consistent estimation in partial linear models with long-memory errors

We consider estimation of beta in the semiparametric regression model y(i) = x(T)(i)beta f(i/n) + epsilon(i) where x(i) = g(i/n) + e(i), f and g are unknown smooth functions and the processes epsilon(i) and e(i) are stationary with short- or long-range dependence. For the case of i.i.d. errors, Speckman (1988) proposed a root n-consistent estimator of beta. In this paper it is shown that, under suitable regularity conditions, this estimator is asymptotically unbiased and root n-consistent even if the errors exhibit long-range dependence. The orders of the finite sample bias and of the required bandwidth depend on the long-memory parameters. Simulations and a data example illustrate the method.