Model Order Selection in System Identi cation: New and Old Techniques | Giulia Prando
| | Abstract | Model order selection has always represented an important and difficult problem, both in system identification and statistics; for these reasons, it has been widely studied in literature. This thesis faces the problem in a system identification perspective, with the aim of providing a quite extensive study of classical and innovative techniques, which are adopted for model order selection. Among the classical methods, cross-validation, information criteria, the F-test and the statistical tests on the residuals are considered. Newly introduced techniques are also evaluated, such as the so-called PUMS criterion (Parsimonious Unfalsifi ed Model Structure Selection), the kernel-based estimation and its connection with the prediction error method approach (PEM). A theoretical description of these methods is provided and accompanied by an experimental analysis, which exploits a versatile data bank, containing both systems and data sets. The order selection methods are not evaluated according to their ability to determine the true order of a system, but to select a complexity which leads to a good reproduction of the input-output properties (impulse response) of the true system. Two combinations of the considered order selection techniques are also introduced and the results based on the data bank prove that the simultaneous adoption of two methods reduces the risk of wrong order choices. Particular attention is also reserved to the tuning of the significance level to be adopted in the order selection criteria based on statistical tests. | | Type | Master's thesis [Academic thesis] | | Year | 2013 | | Publisher | Technical University of Denmark, Department of Applied Mathematics and Computer Science / DTU Co | | Address | Matematiktorvet, Building 303B, DK-2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk | | Series | M.Sc.-2013-86 | | Note | | | Electronic version(s) | [pdf] | | Publication link | http://www.compute.dtu.dk/English.aspx | | BibTeX data | [bibtex] | | IMM Group(s) | Mathematical Statistics |
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