Journal article
Use and Subtleties of Saddlepoint Approximation for Minimum Mean-Square Error Estimation
An integral representation for the minimum mean-square error (MMSE) estimator for a random variable in an observation model consisting of a linear combination of two random variables is derived. The derivation is based on the moment-generating functions for the random variables in the observation model.
The method generalizes so that integral representations For higher-order moments of the posterior of interest can be easily obtained. Two examples are presented that demonstrate how saddle-point approximation can be used to obtain accurate approximations for a MMSE estimator using the derived integral representation.
However, the examples also demonstrate that when two saddle points are close or coalesce, then saddle-point approximation based on isolated saddle points is not valid. A saddle-point approximation based on two close or coalesced saddle points is derived and in the examples, the validity and accuracy of the derivation is demonstrated
Language: | English |
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Publisher: | IEEE |
Year: | 2008 |
Pages: | 5778-5787 |
ISSN: | 15579654 and 00189448 |
Types: | Journal article |
DOI: | 10.1109/TIT.2008.2006375 |
ORCIDs: | Hansen, Lars Kai |