J Austral Math Soc Ser A 48 pp299--319, 1990.

Functional Least Squares Estimators in an Additive Effects Outliers Model

Sunil K. Dhar

Abstract

Consider the additive effects outliers (A.O.) model where one observers Y_j,n = X_j + v_j,n, 0 £ j £ n, with

Xj = rXj-1 + ej,    j = 0, ±1, ±2, ..., |r| < 1.

The sequence of r.v.s {X_j, j £ n} is independent of {v_j,n, 0 £ j £ n} and v_j,n, 0 £ j £ n, are i.i.d. with d.f. (1 - g_n)I[x ³ 0] + g_nL_n(x), x Î R, 0 £ g_n £ 1, where the d.f.s L_n, n ³ 0, are not necessarily known and e_j's are i.i.d.. This paper discusses the asymptotic behaviour 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.

1980 AMS Subject Classification (1985 Revision): 62G05, 62M10

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Authors

Sunil K. Dhar

Department of Mathematics, The University of Alabama, P.O. Box 870350, Tuscaloosa, Alabama 35487-0350, U.S.A.