TY - GEN

T1 - Order statistics approach to estimation of the dimension of the noise subspace

AU - Fishler, Eran

AU - Friedman, Jonathan

AU - Messer, Hagit

N1 - Publisher Copyright:
© 1999 IEEE.

PY - 1999

Y1 - 1999

N2 - Model order selection and in particular determination of the dimension of the noise subspace, is an important problem in statistical signal processing. The discrete nature of the problem puts it in between detection and estimation. Standard tools from detection theory force a solution subject to arbitrary false alarm probability. On the other hand the direct maximum likelihood (ML) approach requires a penalty connection. In this paper we suggest the use of order statistics (OS) approach for the estimation of the dimension of the noise subspace. We show that the likelihood function of the ordered data has a unique non-trivial maximum with respect to the assumed dimension, and therefore we suggest an OS ML estimator. It is based on processing a single ordered sample and is, therefore, very simple. It assumes nothing about the distribution of the signal plus noise and therefore it is robust to the signal model. The suggested approach is demonstrated for i.i.d. exponential noise.

AB - Model order selection and in particular determination of the dimension of the noise subspace, is an important problem in statistical signal processing. The discrete nature of the problem puts it in between detection and estimation. Standard tools from detection theory force a solution subject to arbitrary false alarm probability. On the other hand the direct maximum likelihood (ML) approach requires a penalty connection. In this paper we suggest the use of order statistics (OS) approach for the estimation of the dimension of the noise subspace. We show that the likelihood function of the ordered data has a unique non-trivial maximum with respect to the assumed dimension, and therefore we suggest an OS ML estimator. It is based on processing a single ordered sample and is, therefore, very simple. It assumes nothing about the distribution of the signal plus noise and therefore it is robust to the signal model. The suggested approach is demonstrated for i.i.d. exponential noise.

UR - http://www.scopus.com/inward/record.url?scp=17244364521&partnerID=8YFLogxK

U2 - 10.1109/HOST.1999.778743

DO - 10.1109/HOST.1999.778743

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AN - SCOPUS:17244364521

T3 - Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999

SP - 281

EP - 284

BT - Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 1999 IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999

Y2 - 14 June 1999 through 16 June 1999

ER -