## Abstract

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.

Original language | English |
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Title of host publication | Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 281-284 |

Number of pages | 4 |

ISBN (Electronic) | 0769501400, 9780769501406 |

DOIs | |

State | Published - 1999 |

Externally published | Yes |

Event | 1999 IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999 - Caesarea, Israel Duration: 14 Jun 1999 → 16 Jun 1999 |

### Publication series

Name | Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999 |
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### Conference

Conference | 1999 IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999 |
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Country/Territory | Israel |

City | Caesarea |

Period | 14/06/99 → 16/06/99 |

### Bibliographical note

Publisher Copyright:© 1999 IEEE.