Functional Least Squares Estimators in an Additive Effects Outliers Model

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Abstract

Consider the additive effects outliers (A.O.) model where one observes Yj,n = Xj + vj,n, 0 ≤ j ≤ n, with [formula omitted]. The sequence of r.v.s {Xj,j < n} is independent of {vj,n 0 < j < n} and vj,n 0 ≤ j ≤ n, are i.i.d. with d.f. (1 − γn)I[x ≥ 0] + γnLn(x), x ∊ R, 0 < γn < 1, where the d.f.s Ln, n > 0, are not necessarily known and εj'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 languageEnglish (US)
Pages (from-to)299-319
Number of pages21
JournalJournal of the Australian Mathematical Society
Volume48
Issue number2
DOIs
StatePublished - Apr 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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