| Abstract: | Minimax-rate adaptive nonparametric regression has been intensively studied under the assumption of independent or uncorrelated errors in the literature. In many applications, however, the errors are dependent,including both short-and long-range dependent situations. In such a case, adaptation with respect to the unknown dependence is important. We present a general result in this direction under Gaussian errors. It is assumed that the covariance matrix of the errors is known to be in a list of specifications possibly including independence, short-range dependence and long-range dependence as well. The regression function is known to be in a countable(or uncountablu but well-structured) collection of function classes. Adaptive estimators are constructed to attain the minimax rate of convergence automatically for each function class under each correlation specification in the corresponding lists. |
