Abstract
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)+Γn(t)Z(t) where {Z(t)} is a contaminating process and {Γn(t)} is a switching process such that Γn(t)=1 and 0 with probability γn=γ/√n and -γn=1-γn 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.
