### Abstract

Consider the standard linear model y_{i}=z_{i}β+e_{i}, i=1, 2,..., n, where z_{i} denotes the ith row of an n x p design matrix, β∈ℝ^{p} is an unknown parameter to be estimated and e_{i} are independent random variables with a common distribution function F. The least absolute deviation (LAD) estimate {Mathematical expression} of β is defined as any solution of the minimization problem {Mathematical expression} In this paper Bahadur type representations are obtained for {Mathematical expression} under very mild conditions on F near zero and on z_{i}, i=1,..., n. These results are extended to the case, when {e_{i}} is a mixing sequence. In particular the results are applicable when the residuals e_{i} form a simple autoregressive process.

Original language | English (US) |
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Pages (from-to) | 547-558 |

Number of pages | 12 |

Journal | Probability Theory and Related Fields |

Volume | 83 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 1989 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty