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Minimum distance estimation in an additive effects outliers model. (English) Zbl 0741.62082

Summary: In the additive effects outliers (A.O.) model considered here one observes \(Y_{j,n}=X_ j+v_{j,n}\), \(0\leq j\leq n\), where \(\{X_ j\}\) is the first order autoregressive \([AR(1)]\) process with the autoregressive parameter \(| \rho|<1\). The A.O.’s \(\{v_{j,n}, 0\leq j\leq n\}\) are i.i.d. with distribution function (d.f.) \[ (1- \gamma_ n)I[x\geq 0]+\gamma_ nL_ n(x),\quad x\in \mathbb{R},\quad 0\leq \gamma_ n\leq 1, \] where the d.f.’s \(\{L_ n, n\geq 0\}\) are not necessarily known. This paper discusses existence, asymptotic normality and biases of the class of minimum distance estimators of \(\rho\), defined by H. L. Koul [ibid. 14, 1194-1213 (1986; Zbl 0607.62101)] 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference

Citations:

Zbl 0607.62101
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