### 抜粋

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.

元の言語 | English |
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ページ（範囲） | 282-300 |

ページ数 | 19 |

ジャーナル | Journal of Multivariate Analysis |

巻 | 90 |

発行部数 | 2 |

DOI | |

出版物ステータス | Published - 2004 8 1 |

### ASJC Scopus subject areas

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

## フィンガープリント Discriminant analysis for locally stationary processes' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*Journal of Multivariate Analysis*,

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