Li, Y.-H.Y.-H.LiYEN-HUAN LIPING-CHENG YEH2020-06-112020-06-1120121053587Xhttps://scholars.lib.ntu.edu.tw/handle/123456789/499770https://www.scopus.com/inward/record.uri?eid=2-s2.0-84866514163&doi=10.1109%2fTSP.2012.2208105&partnerID=40&md5=4657941a00a0326067777a7020565cd2It 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.Constrained parameters; Cramér-Rao bound (CRB); Singular Fisher information matrix (FIM)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 matrixjournal article10.1109/TSP.2012.22081052-s2.0-84866514163