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

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 |

### Fingerprint

### 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

### Cite this

**ROBUST REGRESSION AND INTERPOLATION FOR TIME SERIES.** / Taniguchi, Masanobu.

Research output: Contribution to journal › Article

*Journal of Time Series Analysis*, vol. 2, no. 1, pp. 53-62. https://doi.org/10.1111/j.1467-9892.1981.tb00311.x

}

TY - JOUR

T1 - ROBUST REGRESSION AND INTERPOLATION FOR TIME SERIES

AU - Taniguchi, Masanobu

PY - 1981

Y1 - 1981

N2 - 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 Do, 0<ε<1}, where f(x) is a known spectral density and D0 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.

AB - 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 Do, 0<ε<1}, where f(x) is a known spectral density and D0 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.

KW - interpolation

KW - regression spectrum

KW - robust estimation

KW - spectral density

KW - spectrum element

KW - Stationary process

KW - time series regression

UR - http://www.scopus.com/inward/record.url?scp=84986774151&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84986774151&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9892.1981.tb00311.x

DO - 10.1111/j.1467-9892.1981.tb00311.x

M3 - Article

VL - 2

SP - 53

EP - 62

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

SN - 0143-9782

IS - 1

ER -