The estimation of the autocorrelation of a stationary Gaussian time series {
X(
t)} is discussed. The observed time series is, however,
Yn(
t)=
X(
t)+Γ
n(
t)
Z(
t) where {
Z(
t)} is a contaminating process and {Γ
n(
t)} is a switching process such that Γ
n(
t)=1 and 0 with probability γ
n=γ/√
n and
-γ
n=1-γ
n for sample size
n, respectively. Then, we analogically call {
Yn(
t)} to be distributed under a Pitman-type alternative of gross errors against the original process {
X(
t)}. We show the asymptotic normality of the estimator based on a limiter estimating function (c.f. [8], [11]) under this alternative.
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