### 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 |
---|---|

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 |

### Fingerprint

### 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

### Cite this

**DISCRIMINANT ANALYSIS FOR STATIONARY VECTOR TIME SERIES.** / Zhang, Guoqiang; Taniguchi, Masanobu.

Research output: Contribution to journal › Article

*Journal of Time Series Analysis*, vol. 15, no. 1, pp. 117-126. https://doi.org/10.1111/j.1467-9892.1994.tb00180.x

}

TY - JOUR

T1 - DISCRIMINANT ANALYSIS FOR STATIONARY VECTOR TIME SERIES

AU - Zhang, Guoqiang

AU - Taniguchi, Masanobu

PY - 1994

Y1 - 1994

N2 - Abstract. In this paper, we shall consider the case where a stationary vector process {Xt} belongs to one of two categories described by two hypotheses π1 and π2. These hypotheses specify that {Xt} has spectral density matrices f(Λ) and g(Λ) under π1 and π2, respectively. Although Gaussianity of {Xt} 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.

AB - Abstract. In this paper, we shall consider the case where a stationary vector process {Xt} belongs to one of two categories described by two hypotheses π1 and π2. These hypotheses specify that {Xt} has spectral density matrices f(Λ) and g(Λ) under π1 and π2, respectively. Although Gaussianity of {Xt} 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.

KW - classification criterion

KW - innovation‐free

KW - misclassification probability

KW - non‐Gaussian robust

KW - spectral density matrix

KW - Vector linear process

UR - http://www.scopus.com/inward/record.url?scp=84981422060&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84981422060&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9892.1994.tb00180.x

DO - 10.1111/j.1467-9892.1994.tb00180.x

M3 - Article

AN - SCOPUS:84981422060

VL - 15

SP - 117

EP - 126

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

SN - 0143-9782

IS - 1

ER -