## Abstract

Consider the additive effects outliers (A.O.) model where one observes Y_{j,n} = X_{j} + v_{j,n}, 0 ≤ j ≤ n, with [formula omitted]. The sequence of r.v.s {X_{j},j < n} is independent of {v_{j,n} 0 < j < n} and v_{j,n} 0 ≤ j ≤ n, are i.i.d. with d.f. (1 − γ_{n})I[x ≥ 0] + γ_{n}L_{n}(x), x ∊ R, 0 < γ_{n} < 1, where the d.f.s L_{n}, n > 0, are not necessarily known and ε_{j}'s are i.i.d. This paper discusses the asymptotic behavior of functional least squares estimators under the above model. Uniform consistency and uniform strong consistency of these estimators are proven. The weak convergence of these estimators to a Gaussian process and their asymptotic biases are also discussed under the above A.O. model.

Original language | English (US) |
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Pages (from-to) | 299-319 |

Number of pages | 21 |

Journal | Journal of the Australian Mathematical Society |

Volume | 48 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1990 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)