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) |
|---|---|
| Pages (from-to) | 227-244 |
| Number of pages | 18 |
| Journal | Science China Mathematics |
| Volume | 62 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1 2019 |
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Keywords
- 62C20
- 62G08
- adaptive estimation
- long-range dependence
- nonparametric regression
- rate of convergence
Cite this
Minimax-rate adaptive nonparametric regression with unknown correlations of errors. / Yang, Guowu; Yang, Yuhong.
In: Science China Mathematics, Vol. 62, No. 2, 01.02.2019, p. 227-244.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Minimax-rate adaptive nonparametric regression with unknown correlations of errors
AU - Yang, Guowu
AU - Yang, Yuhong
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
KW - 62C20
KW - 62G08
KW - adaptive estimation
KW - long-range dependence
KW - nonparametric regression
KW - rate of convergence
UR - http://www.scopus.com/inward/record.url?scp=85060235621&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85060235621&partnerID=8YFLogxK
U2 - 10.1007/s11425-018-9394-x
DO - 10.1007/s11425-018-9394-x
M3 - Article
AN - SCOPUS:85060235621
VL - 62
SP - 227
EP - 244
JO - Science China Mathematics
JF - Science China Mathematics
SN - 1674-7283
IS - 2
ER -