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Suppose that I can do a Karhunen-Loeve expansion of a log-likelihood function $p(\bf{x};\theta)$ into N terms and that these accounts for a fraction $1-\delta$ of the total energy. Now consider estimation of $\theta$ based on the expansion.

Two questions: 1. Can I obtain a bound on the error of MLE based on the expansion to the true MLE? 2. Can I derive a new CRLB for the mismatched model?

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  • $\begingroup$ I think that it is easy to observe what happens with the Fisher information (so as for the CRLB) when KL decomposition is used. $\endgroup$
    – mikitov
    Commented Jun 23, 2015 at 12:30

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