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March, 1991 Minimum Distance Estimation in an Additive Effects Outliers Model
Sunil K. Dhar
Ann. Statist. 19(1): 205-228 (March, 1991). DOI: 10.1214/aos/1176347977


In the additive effects outliers (A.O.) model considered here one observes $Y_{j,n} = X_j + \upsilon_{j,n}, 0 \leq j \leq n$, where $\{X_j\}$ is the first order autoregressive [AR(1)] process with the autoregressive parameter $|\rho| < 1$. The A.O.'s $\{\upsilon_{j,n}, 0 \leq j \leq n\}$ are i.i.d. with distribution function (d.f.) $(1 - \gamma_n)I\lbrack x \geq 0\rbrack + \gamma_n L_n(x), x \in \mathbb{R}, 0 \leq \gamma_n \leq 1$, where the d.f.'s $\{L_n, n \geq 0\}$ are not necessarily known. This paper discusses the existence, the asymptotic normality and biases of the class of minimum distance estimators of $\rho$, defined by Koul, under the A.O. model. Their influence functions are computed and are shown to be directly proportional to the asymptotic biases. Thus, this class of estimators of $\rho$ is shown to be robust against A.O. model.


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Sunil K. Dhar. "Minimum Distance Estimation in an Additive Effects Outliers Model." Ann. Statist. 19 (1) 205 - 228, March, 1991.


Published: March, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0741.62082
MathSciNet: MR1091846
Digital Object Identifier: 10.1214/aos/1176347977

Primary: 62G05
Secondary: 62M10

Keywords: Additive outlier , asymptotic bias , influence function

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 1 • March, 1991
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