Use and Subtleties of Saddlepoint Approximation for Minimum Mean-Square Error Estimation

Publication: Research - peer-reviewJournal article – Annual report year: 2008

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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
Original languageEnglish
JournalIEEE Transactions on Information Theory
Publication date2008
Volume54
Issue12
Pages5778-5787
ISSN0018-9448
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 0

Keywords

  • moment-generating functions, monkey saddle point, Coalescing saddle points, minimum mean-square error estimation (MMSE), saddle-point approximation
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