### Abstract

Gaussian assumption is the most well-known and widely used distribution in many fields such as engineering, statistics, and physics. One of the major reasons why the Gaussian distribution has become so prominent is because of the central limit theorem (CLT) and the fact that the distribution of noise in numerous engineering systems is well captured by the Gaussian distribution. Moreover, features such as analytical tractability and easy generation of other distributions from the Gaussian distribution contributed further to the popularity of Gaussian distribution. Especially, when there is no information about the distribution of observations, Gaussian assumption appears as the most conservative choice. This follows from the fact that the Gaussian distribution minimizes the Fisher information, which is the inverse of the Cram?r-Rao lower bound (CRLB) (or equivalently stated, the Gaussian distribution maximizes the CRLB). Therefore, any optimization based on the CRLB under the Gaussian assumption can be considered to be min-max optimal in the sense of minimizing the largest CRLB (see [1] and the references cited therein).

Original language | English |
---|---|

Article number | 6494684 |

Pages (from-to) | 183-186 |

Number of pages | 4 |

Journal | IEEE Signal Processing Magazine |

Volume | 30 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2013 |

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### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering
- Applied Mathematics

### Cite this

*IEEE Signal Processing Magazine*,

*30*(3), 183-186. [6494684]. https://doi.org/10.1109/MSP.2013.2238691

**Gaussian assumption : The least favorable but the most useful.** / Park, Sangwoo; Serpedin, Erchin; Qaraqe, Khalid.

Research output: Contribution to journal › Article

*IEEE Signal Processing Magazine*, vol. 30, no. 3, 6494684, pp. 183-186. https://doi.org/10.1109/MSP.2013.2238691

}

TY - JOUR

T1 - Gaussian assumption

T2 - The least favorable but the most useful

AU - Park, Sangwoo

AU - Serpedin, Erchin

AU - Qaraqe, Khalid

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Gaussian assumption is the most well-known and widely used distribution in many fields such as engineering, statistics, and physics. One of the major reasons why the Gaussian distribution has become so prominent is because of the central limit theorem (CLT) and the fact that the distribution of noise in numerous engineering systems is well captured by the Gaussian distribution. Moreover, features such as analytical tractability and easy generation of other distributions from the Gaussian distribution contributed further to the popularity of Gaussian distribution. Especially, when there is no information about the distribution of observations, Gaussian assumption appears as the most conservative choice. This follows from the fact that the Gaussian distribution minimizes the Fisher information, which is the inverse of the Cram?r-Rao lower bound (CRLB) (or equivalently stated, the Gaussian distribution maximizes the CRLB). Therefore, any optimization based on the CRLB under the Gaussian assumption can be considered to be min-max optimal in the sense of minimizing the largest CRLB (see [1] and the references cited therein).

AB - Gaussian assumption is the most well-known and widely used distribution in many fields such as engineering, statistics, and physics. One of the major reasons why the Gaussian distribution has become so prominent is because of the central limit theorem (CLT) and the fact that the distribution of noise in numerous engineering systems is well captured by the Gaussian distribution. Moreover, features such as analytical tractability and easy generation of other distributions from the Gaussian distribution contributed further to the popularity of Gaussian distribution. Especially, when there is no information about the distribution of observations, Gaussian assumption appears as the most conservative choice. This follows from the fact that the Gaussian distribution minimizes the Fisher information, which is the inverse of the Cram?r-Rao lower bound (CRLB) (or equivalently stated, the Gaussian distribution maximizes the CRLB). Therefore, any optimization based on the CRLB under the Gaussian assumption can be considered to be min-max optimal in the sense of minimizing the largest CRLB (see [1] and the references cited therein).

UR - http://www.scopus.com/inward/record.url?scp=85032752349&partnerID=8YFLogxK

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U2 - 10.1109/MSP.2013.2238691

DO - 10.1109/MSP.2013.2238691

M3 - Article

VL - 30

SP - 183

EP - 186

JO - IEEE Signal Processing Magazine

JF - IEEE Signal Processing Magazine

SN - 1053-5888

IS - 3

M1 - 6494684

ER -