TY - GEN
T1 - Recursive estimation of a locally stationary process
AU - Moulines, E.
AU - Roueff, F.
AU - Priouret, P.
N1 - Publisher Copyright:
© 2003 IEEE.
PY - 2003/1/1
Y1 - 2003/1/1
N2 - We consider the problem of estimating the parameters of a locally stationary autoregressive process. This approach models the time evolution of the spectral content of a time series by a [0,1] → ℝd x ℝ+ mapping of d linear prediction coefficients and the innovation variance. The identification problem for this model fits the classical non-parametric curve estimation theory. In this contribution we focus on recursive estimators and more particularly on the LMS (least mean square) algorithm. This estimator is based on a stochastic gradient approach. A precise study of its asymptotic behavior is proposed. It turns out that this estimator achieves the minimax rate only in a limited range of smoothness classes. We propose a bias reduction method which allows to achieve this rate in a wider range of smoothness classes.
AB - We consider the problem of estimating the parameters of a locally stationary autoregressive process. This approach models the time evolution of the spectral content of a time series by a [0,1] → ℝd x ℝ+ mapping of d linear prediction coefficients and the innovation variance. The identification problem for this model fits the classical non-parametric curve estimation theory. In this contribution we focus on recursive estimators and more particularly on the LMS (least mean square) algorithm. This estimator is based on a stochastic gradient approach. A precise study of its asymptotic behavior is proposed. It turns out that this estimator achieves the minimax rate only in a limited range of smoothness classes. We propose a bias reduction method which allows to achieve this rate in a wider range of smoothness classes.
KW - Autoregressive processes
KW - Density functional theory
KW - Estimation theory
KW - Least squares approximation
KW - Minimax techniques
KW - Parameter estimation
KW - Recursive estimation
KW - Signal processing algorithms
KW - Stochastic processes
KW - Technological innovation
U2 - 10.1109/SSP.2003.1289352
DO - 10.1109/SSP.2003.1289352
M3 - Conference contribution
AN - SCOPUS:84947574006
T3 - IEEE Workshop on Statistical Signal Processing Proceedings
SP - 110
EP - 113
BT - Proceedings of the 2003 IEEE Workshop on Statistical Signal Processing, SSP 2003
PB - IEEE Computer Society
T2 - IEEE Workshop on Statistical Signal Processing, SSP 2003
Y2 - 28 September 2003 through 1 October 2003
ER -