### Abstract

In this paper, we discuss discriminant analysis for locally stationary processes, which constitute a class of non-stationary processes. Consider the case where a locally stationary process {X_{t,T}} belongs to one of two categories described by two hypotheses π_{1} and π_{2}. Here T is the length of the observed stretch. These hypotheses specify that {X_{t,T}} has time-varying spectral densities f(u,λ) and g(u,λ) under π_{1} and π_{2}, respectively. Although Gaussianity of {X_{t,T}} is not assumed, we use a classification criterion D(f:g), which is an approximation of the Gaussian likelihood ratio for {X_{t,T}} between π_{1} and π_{2}. Then it is shown that D(f:g) is consistent, i.e., the misclassification probabilities based on D(f:g) converge to zero as T→∞. Next, in the case when g(u,λ) is contiguous to f(u,λ), we evaluate the misclassification probabilities, and discuss non-Gaussian robustness of D(f:g). Because the spectra depend on time, the features of non-Gaussian robustness are different from those for stationary processes. It is also interesting to investigate the behavior of D(f:g) with respect to infinitesimal perturbations of the spectra. Introducing an influence function of D(f:g), we illuminate its infinitesimal behavior. Some numerical studies are given.

Original language | English |
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Pages (from-to) | 282-300 |

Number of pages | 19 |

Journal | Journal of Multivariate Analysis |

Volume | 90 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 Aug 1 |

### Keywords

- Classification criterion
- Influence function
- Least favorable spectral density
- Locally stationary vector process
- Misclassification probability
- Non-Gaussian robust
- Time-varying spectral density matrix

### ASJC Scopus subject areas

- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty

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## Cite this

*Journal of Multivariate Analysis*,

*90*(2), 282-300. https://doi.org/10.1016/j.jmva.2003.08.002