### Abstract

Abstract. In this paper, we shall consider the case where a stationary vector process {X_{t}} belongs to one of two categories described by two hypotheses π_{1} and π_{2}. These hypotheses specify that {X_{t}} has spectral density matrices f(Λ) and g(Λ) under π_{1} and π_{2}, respectively. Although Gaussianity of {X_{t}} is not assumed, we can formally make the Gaussian likelihood ratio (GLR) based on X(1),…X(T). Then an approximation I(f:g) of the GLR is given in terms of f(Λ) and g(Λ). If f(Λ) and g(Λ) are known, we can use I(f:g) as a classification statistic. It is shown that I(f:g) is a consistent classification criterion in the sense that the misclassification probabilities converge to zero as T→∝. When g is contiguous to f, we discuss non‐Gaussian robustness of I(f:g). A sufficient condition for the non‐Gaussian robustness will be given. Also a numerical example will be given.

Original language | English |
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Pages (from-to) | 117-126 |

Number of pages | 10 |

Journal | Journal of Time Series Analysis |

Volume | 15 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1994 |

Externally published | Yes |

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### Keywords

- classification criterion
- innovation‐free
- misclassification probability
- non‐Gaussian robust
- spectral density matrix
- Vector linear process

### ASJC Scopus subject areas

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