## Abstract

Huber (1964) found the minimax-variance M-estimate of location under the assumption that the scale parameter is known; Li and Zamar (1991) extended this result to the case when the scale is unknown. We consider the robust estimation of the regression coefficients (β_{1} , . . . , β_{p}) when the scale and the intercept parameters are unknown. The minimax-variance estimates of (β_{1} , . . . , β_{p}) with respect to the trace of their asymptotic covariance matrix are derived. The maximum is taken over ∈-contamination neighbourhoods of a central regression model with Gaussian errors (asymmetric contamination is allowed), and the minimum is taken over a large class of generalized M-estimates of regression of the Mallow type. The optimal choice of estimates for the nuisance parameters (scale and intercept) is also considered.

Original language | English (US) |
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Pages (from-to) | 193-206 |

Number of pages | 14 |

Journal | Canadian Journal of Statistics |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1996 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty