Minimax-rate adaptive nonparametric regression with unknown correlations of errors

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（2）
• 页码范围: 227-244
• 页数: 18页
• 语种: 英文

摘要

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 uncountable 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.