## Abstract

Abstract. In this paper we shall consider the interpolation problem under the condition that the spectral density of a stationary process concerned is vaguely known (i.e., Huber's ε ‐contaminated model). Then we can get a minimax robust interpolator for the class of spectral densities S={ g:g(x)=(1‐ε)f(x)+εh(x)ε Ar D_{o}, 0<ε<1}, where f(x) is a known spectral density and D_{0} is a certain class of spectral densities. Also we shall consider the time series regression problem under the condition that the residual spectral density is vaguely known. Then we can get a minimax robust regression coefficient estimate for the class of the residual spectral densities S.

Original language | English |
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Pages (from-to) | 53-62 |

Number of pages | 10 |

Journal | Journal of Time Series Analysis |

Volume | 2 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1981 |

Externally published | Yes |

## Keywords

- interpolation
- regression spectrum
- robust estimation
- spectral density
- spectrum element
- Stationary process
- time series regression

## ASJC Scopus subject areas

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