### Abstract

The tail behavior of the least-squares estimator in the linear regression model was studied in He et al. (Econometrica 58 (1990) 1195) under a fixed design for finite n. We now consider a random design matrix X_{n} and the case n→∞ and study the probability P_{0}(max_{1≤i≤n}|x_{i}′β̂ _{n}|≥γ_{n}) with γ_{n}=F^{-1}(1-1/n), a population analog of the maximal error. Unlike in the situation with fixed n and γ→∞, for n→∞ we find fairly good tail behavior of LSE for normal F, for both fixed and random designs, even under heavy-tailed distribution for X_{n}.

Original language | English (US) |
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Pages (from-to) | 377-384 |

Number of pages | 8 |

Journal | Statistics and Probability Letters |

Volume | 55 |

Issue number | 4 |

DOIs | |

State | Published - Dec 15 2001 |

### Keywords

- Domain of attraction
- Extreme values
- Least-squares estimator
- Tail behavior

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Jurečková, J., Koenker, R., & Portnoy, S. (2001). Tail behavior of the least-squares estimator.

*Statistics and Probability Letters*,*55*(4), 377-384. https://doi.org/10.1016/S0167-7152(01)00137-7