TY - JOUR
T1 - Shrinkage estimation for multivariate time series
AU - Liu, Yan
AU - Tanida, Yoshiyuki
AU - Taniguchi, Masanobu
N1 - Funding Information:
Yan Liu was supported by JSPS Grant-in-Aid for Scientific Research (C) 20K11719. Masanobu Taniguchi would like to thank the Research Institute for Science and Engineering, Waseda University, and JSPS Grant-in-Aid for Scientific Research (S) 18H05290. We also express our gratitude to the Institute for Mathematical Science (IMS) in Waseda University for their kind support.
Funding Information:
Yan Liu was supported by JSPS Grant-in-Aid for Scientific Research (C) 20K11719. Masanobu Taniguchi would like to thank the Research Institute for Science and Engineering, Waseda University, and JSPS Grant-in-Aid for Scientific Research (S) 18H05290. We also express our gratitude to the Institute for Mathematical Science (IMS) in Waseda University for their kind support.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2021/10
Y1 - 2021/10
N2 - This paper deals with shrinkage estimators for the mean of p-dimensional Gaussian stationary processes. The shrinkage estimators are expressed by a shrinkage function, including the sample mean and the James–Stein estimator as special cases. We evaluate the mean squared error of such shrinkage estimators from the true mean of a p-dimensional Gaussian vector stationary process with p≥ 3. A sufficient condition for shrinkage estimators improving the mean squared error upon the sample mean is given in terms of the shrinkage function and the spectral density matrix. In addition, a shrinkage estimator, providing the most significant improvement to the sample mean, is proposed as a theoretical result. The remarkable performance of the proposed shrinkage estimator, compared with the sample mean and the James–Stein estimator, is illustrated by a thorough numerical simulation. A real data analysis also witnesses the applicability of the proposed estimator for multivariate time series.
AB - This paper deals with shrinkage estimators for the mean of p-dimensional Gaussian stationary processes. The shrinkage estimators are expressed by a shrinkage function, including the sample mean and the James–Stein estimator as special cases. We evaluate the mean squared error of such shrinkage estimators from the true mean of a p-dimensional Gaussian vector stationary process with p≥ 3. A sufficient condition for shrinkage estimators improving the mean squared error upon the sample mean is given in terms of the shrinkage function and the spectral density matrix. In addition, a shrinkage estimator, providing the most significant improvement to the sample mean, is proposed as a theoretical result. The remarkable performance of the proposed shrinkage estimator, compared with the sample mean and the James–Stein estimator, is illustrated by a thorough numerical simulation. A real data analysis also witnesses the applicability of the proposed estimator for multivariate time series.
KW - James–Stein estimator
KW - Multivariate stationary processes
KW - Sample mean
KW - Shrinkage estimation
KW - Shrinkage function
KW - Spectral density matrix
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U2 - 10.1007/s11203-021-09248-2
DO - 10.1007/s11203-021-09248-2
M3 - Article
AN - SCOPUS:85110713066
SN - 1387-0874
VL - 24
SP - 733
EP - 751
JO - Statistical Inference for Stochastic Processes
JF - Statistical Inference for Stochastic Processes
IS - 3
ER -