Let Z1,..., Zn be i.i.d. according to a continuous distribution symmetric about , and let T(1) <

Let Z1,..., Zn be i.i.d. according to a continuous distribution symmetric about θ, and let T(1) < ··· < T(M) be the ordered set of M = 2n − 1 subsamples; (Zi1 +···+ Zir )/r, r ≥ 1. If T(0) = −∞, T(M+1) = ∞, then Pθ[T(i) < θ < T(i+1)] =

1 M + 1 for all i = 0, 1,..., M.

[Hartigan (1969).]