From the point of the unbiased estimator, there will still be a lower bound of covariance which will have nothing to do with FIM when it's singular, so I want to know are there some references about what's the consequences when FIM is not invertible, not limited to Cramer-Rao lower bound, I just want to know as systematically as possible the consequences?
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1$\begingroup$ Related SE post: stats.stackexchange.com/q/273303/362671. $\endgroup$– User1865345Commented Aug 20, 2022 at 12:05
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1$\begingroup$ Also an interesting article to have a glance at: An Interpretation of the Moore-Penrose Generalized Inverse of a Singular Fisher Information Matrix. $\endgroup$– User1865345Commented Aug 20, 2022 at 12:06
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