### Abstract

In the general linear model with independent and identically distributed errors and distribution function F, the estimator which minimizes the sum of absolute residuals is demonstrated to be consistent and asymptotically Gaussian with covariance matrix ω^{2}Q^{−1}, where Q = lim T^{−1}X′X and ω^{2}is the asymptotic variance of the ordinary sample median from samples with distribution F. Thus the least absolute error estimator has strictly smaller asymptotic confidence ellipsoids than the least squares estimator for linear models from any F for which the sample median is a more efficient estimator of location than the sample mean.

Original language | English (US) |
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Pages (from-to) | 618-622 |

Number of pages | 5 |

Journal | Journal of the American Statistical Association |

Volume | 73 |

Issue number | 363 |

DOIs | |

State | Published - Sep 1978 |

### Keywords

- Asymptotic distribution theory
- Least absolute error estimators
- Linear models

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Bassett, G., & Koenker, R. (1978). Asymptotic theory of least absolute error regression.

*Journal of the American Statistical Association*,*73*(363), 618-622. https://doi.org/10.1080/01621459.1978.10480065