### 抜粋

Suppose that {z(t)} is a non-Gaussian vector stationary process with spectral density matrix f(λ). In this paper we consider the testing problem H:∫^{π}_{-π} K{f(λ)} dλ = c against A: ∫^{π}_{-π} K{f(λ)} dλ ≠ c, where K{·} is an appropriate function and c is a given constant. For this problem we propose a test T_{n} based on ∫^{π}_{-π} K{f̂_{n}(λ)} dλ, where f̂_{n}(λ) is a nonparametric spectral estimator of f(λ), and we define an efficacy of T_{n} under a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectra f^{Z}_{4} of z(t). If it does not depend on f^{Z}_{4}, we say that T_{n} is non-Gaussian robust. We will give sufficient conditions for T_{n} to be non-Gaussian robust. Since our test setting is very wide we can apply the result to many problems in time series. We discuss interrelation analysis of the components of {z(t)} and eigenvalue analysis of f(λ). The essential point of our approach is that we do not assume the parametric form of f(λ). Also some numerical studies are given and they confirm the theoretical results.

元の言語 | English |
---|---|

ページ（範囲） | 259-283 |

ページ数 | 25 |

ジャーナル | Journal of Multivariate Analysis |

巻 | 56 |

発行部数 | 2 |

DOI | |

出版物ステータス | Published - 1996 2 |

### フィンガープリント

### ASJC Scopus subject areas

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

### これを引用

*Journal of Multivariate Analysis*,

*56*(2), 259-283. https://doi.org/10.1006/jmva.1996.0014