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

Publication: Research - peer-review › Journal article – Annual report year: 2008

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**Use and Subtleties of Saddlepoint Approximation for Minimum Mean-Square Error Estimation.** / Beierholm, Thomas; Nuttall, Albert H.; Hansen, Lars Kai.

Publication: Research - peer-review › Journal article – Annual report year: 2008

### Harvard

*IEEE Transactions on Information Theory*, vol 54, no. 12, pp. 5778-5787., 10.1109/TIT.2008.2006375

### APA

*IEEE Transactions on Information Theory*,

*54*(12), 5778-5787. 10.1109/TIT.2008.2006375

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*IEEE Transactions on Information Theory*. 2008, 54(12). 5778-5787. Available: 10.1109/TIT.2008.2006375

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### RIS

TY - JOUR

T1 - Use and Subtleties of Saddlepoint Approximation for Minimum Mean-Square Error Estimation

A1 - Beierholm,Thomas

A1 - Nuttall,Albert H.

A1 - Hansen,Lars Kai

AU - Beierholm,Thomas

AU - Nuttall,Albert H.

AU - Hansen,Lars Kai

PB - I E E E

PY - 2008

Y1 - 2008

N2 - 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

AB - 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

KW - moment-generating functions

KW - monkey saddle point

KW - Coalescing saddle points

KW - minimum mean-square error estimation (MMSE)

KW - saddle-point approximation

U2 - 10.1109/TIT.2008.2006375

DO - 10.1109/TIT.2008.2006375

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 12

VL - 54

SP - 5778

EP - 5787

ER -