MINIMUM DISTANCE ESTIMATION IN AN ADDITIVE EFFECTS OUTLIERS MODEL

• 成果类型: Article
• 署名作者: DHAR, SK
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176347977
• 发表日期: 1991
• 页码: 205-228
• 关键词: time-series; linear-regression

摘要

In the additive effects outliers (A.O.) model considered here one observes Y(j,n) = X(j) + V(j,n), O less-than-or-equal-to j less-than-or-equal-to n, where {X(j)} is the first order autoregressive [AR(1)] process with the autoregressive parameter \rho\ < 1. The A.O.'s {V(j,n), O less-than-or-equal-to n} are i.i.d. with distribution function (d.f.) (1 - gamma-n)I[x greater-than-or-equal-to 0] + gamma-nL(n)(x), x epsilon R, 0 less-than-or-equal-to gamma-n less-than-or-equal-to 1, where the d.f.'s {L(n), n greater-than-or-equal-to 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.