### Abstract

This paper proposes a selection procedure to estimate the multiplicity of the smallest eigenvalue of the covariance matrix. The unknown number of signals present in a radar data can be formulated as the difference between the total number of components in the observed multivariate data vector and the multiplicity of the smallest eigenvalue. In the observed multivariate data, the smallest eigenvalues of the sample covariance matrix may in fact be grouped about some nominal value, as opposed to being identically equal. We propose a selection procedure to estimate the multiplicity of the common smallest eigenvalue, which is significantly smaller than the other eigenvalues. We derive the probability of a correct selection, P(CS), and the least favorable configuration (LFC) for our procedures. Under the LFC, the P(CS) attains its minimum over the preference zone of all eigenvalues. Therefore, a minimum sample size can be determined from the P(CS) under the LFC, P(CS\LFC), in order to implement our new procedure with a guaranteed probability requirement. Numerical examples are presented in order to illustrate our proposed procedure.

Original language | English (US) |
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Pages (from-to) | 299-311 |

Number of pages | 13 |

Journal | Journal of Statistical Planning and Inference |

Volume | 105 |

Issue number | 2 |

DOIs | |

State | Published - Jul 1 2002 |

### Keywords

- Correct selection
- Least favorable configuration
- Multiplicity of the smallest eigenvalue
- Multivariate normal distribution

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics