https://scholars.lib.ntu.edu.tw/handle/123456789/499770
標題: | An interpretation of the moore-penrose generalized inverse of a singular fisher information matrix | 作者: | Li, Y.-H. YEN-HUAN LI PING-CHENG YEH |
關鍵字: | Constrained parameters; Cramér-Rao bound (CRB); Singular Fisher information matrix (FIM) | 公開日期: | 2012 | 卷: | 60 | 期: | 10 | 起(迄)頁: | 5532-5536 | 來源出版物: | IEEE Transactions on Signal Processing | 摘要: | It is proved that in a non-Bayesian parametric estimation problem, if the Fisher information matrix (FIM) is singular, unbiased estimators for the unknown parameter will not exist. Cramér-Rao bound (CRB), a popular tool to lower bound the variances of unbiased estimators, seems inapplicable in such situations. In this correspondence, we show that the Moore-Penrose generalized inverse of a singular FIM can be interpreted as the CRB corresponding to the minimum variance among all choices of minimum constraint functions. This result ensures the logical validity of applying the Moore-Penrose generalized inverse of an FIM as the covariance lower bound when the FIM is singular. Furthermore, the result can be applied as a performance bound on the joint design of constraint functions and unbiased estimators. © 2012 IEEE. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/499770 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84866514163&doi=10.1109%2fTSP.2012.2208105&partnerID=40&md5=4657941a00a0326067777a7020565cd2 |
ISSN: | 1053587X | DOI: | 10.1109/TSP.2012.2208105 | SDG/關鍵字: | Constrained parameters; Constraint functions; Joint designs; Lower bounds; Minimum variance; Moore-Penrose generalized inverse; Parametric estimation; Performance bounds; Singular fisher information; Unbiased estimator; Unknown parameters; Estimation; Fisher information matrix |
顯示於: | 電機工程學系 |
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