By Abdelhak M. Zoubir, Mats Viberg, Rama Chellappa and Sergios Theodoridis (Eds.)

ISBN-10: 0124115977

ISBN-13: 9780124115972

This 3rd quantity of a 5 quantity set, edited and authored via global major specialists, offers a evaluation of the rules, equipment and methods of vital and rising learn themes and applied sciences in array and statistical sign processing.

With this reference resource you will:

- Quickly snatch a brand new sector of research
- Understand the underlying rules of a subject matter and its application
- Ascertain how an issue pertains to different components and examine of the study concerns but to be resolved

- Quick educational reports of vital and rising themes of study in array and statistical sign processing
- Presents center ideas and exhibits their application
- Reference content material on middle ideas, applied sciences, algorithms and purposes
- Comprehensive references to magazine articles and different literature on which to construct additional, extra particular and distinctive wisdom
- Edited by way of leading people in the sector who, via their popularity, were capable of fee specialists to write down on a specific topic

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**Extra info for Array and Statistical Signal Processing**

**Example text**

Since (1/2) ln N > 1 already at small sample lengths (N ≥ 8), the MDL method is less prone to overfitting the data compared to the AIC. Note that first term in the MDL and AIC criterions above is simply the GLRT statistic m . Wax and Kailath [15] showed the MDL rule consistent in choosing the true dimensionality whereas the AIC tends to overestimate the dimensionality (in the large sample limit). Later [34] proved the consistency of the MDL rule when the CN assumption does not hold. 6 Conclusions In this section, we provided an overview of model order estimation methods.

In some special cases, the approximation of stochastic complexity and BIC leads to the same criterion. Detailed descriptions of the MDL method can be found in [1,4]. The MDL method does not make any assumptions on the underlying distribution of the data. In fact, it is considered to be less important since the task at hand is not to estimate the distribution that generated the data but rather to extract useful information or model from the data that facilitates by compressing it efficiently. However, codes used for compressing data and the probability mass functions are related.

2) the detection 2 . 14). Let us now derive the AIC and MDL criteria. 16) can be written compactly as n(M − m) ln (m) up to irrelevant additive constant not dependent on m. 15), we have the result that the AIC and the MDL criteria can be written in the following forms: AIC(m) = −2n(M − m) ln (m) + 2m(2M − m), MDL(m) = −2n(M − m) ln (m) + 2m(2M − m) · ln N . , the dimensionality of the signal subspace m, is found by choosing m ∈ {0, 1, . . , M − 1} that minimizes the AIC/MDL criterion above. As already pointed out, the penalty term of the MDL is (1/2) ln N times the penalty term of AIC.

### Array and Statistical Signal Processing by Abdelhak M. Zoubir, Mats Viberg, Rama Chellappa and Sergios Theodoridis (Eds.)

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