论文信息 - On the convergence of pseudo-linear regression algorithms

On the convergence of pseudo-linear regression algorithms

The convergence properties of a general iterative (off-line) pseudo-linear regression (PLR) algorithm are examined. It is found that the basic form of the algorithm converges under quite restrictive conditions. A simple modification of the algorithm is then proposed which relaxes the convergence conditions considerably. The refined PLR algorithm converges under precisely the same conditions as the well-known recursive (on-line) PLR procedure. The problem of monitoring the algorithm to guarantee the stability of estimated models is also discussed. A modified PLR algorithm which does not require monitoring is proposed, and its convergence properties analysed. Finally, some numerical examples illustrating the main theoretical results are included.

[1] Lennart Ljung,et al. On positive real transfer functions and the convergence of some recursive schemes , 1977 .

[2] Torsten Söderström,et al. Eigenvalue location of certain matrices arising in convergence analysis problems , 1982, Autom..

[3] Jan Holst. Adaptive Prediction and Recursive Estimation , 1977 .

[4] L. Ljung,et al. Counterexamples to general convergence of a commonly used recursive identification method , 1975 .

[5] D. Hendry. The structure of simultaneous equations estimators , 1976 .

[6] T. Söderström,et al. On the asymptotic accuracy of pseudo-linear regression algorithms , 1984 .

[7] L. Taylor,et al. Three-Pass Least Squares: A Method for Estimating Models with a Lagged Dependent Variable , 1964 .

[8] T. Hsia,et al. On least squares algorithms for system parameter identification , 1976 .

[9] P. Young. The use of linear regression and related procedures for the identification of dynamic processes , 1968 .

[10] V. Panuska. An adaptive recursive-least-squares identification algorithm , 1969 .

[11] Lennart Ljung,et al. A theoretical analysis of recursive identification methods , 1978, Autom..

[12] M. S Ahmed. Rapid parameter estimation algorithms using the ELS principle , 1982 .

[13] V. Solo. The convergence of AML , 1979 .

[14] Y. Gupta,et al. Least Squares Variant of the Dhrymes Two-Step Estimation Procedure of the Distributed Lag Model , 1969 .