Translation-invariant estimator
= Translation-invariant estimator
A location estimator $T_n$ is translation-invariant when
$$
T_n(x_1+a,\ldots,x_n+a)=T_n(x_1,\ldots,x_n)+a
$$
for every real shift $a$.
= Translation-invariant estimator
A location estimator $T_n$ is translation-invariant when
$$
T_n(x_1+a,\ldots,x_n+a)=T_n(x_1,\ldots,x_n)+a
$$
for every real shift $a$.