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 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.
Original language | English (US) |
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Pages (from-to) | 227-244 |
Number of pages | 18 |
Journal | Science China Mathematics |
Volume | 62 |
Issue number | 2 |
DOIs | |
State | Published - Feb 1 2019 |
Bibliographical note
Publisher Copyright:© 2019, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.
Keywords
- 62C20
- 62G08
- adaptive estimation
- long-range dependence
- nonparametric regression
- rate of convergence