Minimum Distance Estimation in an Additive Effects Outliers Model
Dhar, Sunil K.
Ann. Statist., Tome 19 (1991) no. 1, p. 205-228 / Harvested from Project Euclid
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.
Publié le : 1991-03-14
Classification:  Additive outlier,  asymptotic bias,  influence function,  62G05,  62M10
@article{1176347977,
     author = {Dhar, Sunil K.},
     title = {Minimum Distance Estimation in an Additive Effects Outliers Model},
     journal = {Ann. Statist.},
     volume = {19},
     number = {1},
     year = {1991},
     pages = { 205-228},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176347977}
}
Dhar, Sunil K. Minimum Distance Estimation in an Additive Effects Outliers Model. Ann. Statist., Tome 19 (1991) no. 1, pp.  205-228. http://gdmltest.u-ga.fr/item/1176347977/