If X and (-1)X both have the same distribution function F, defined on Rp, then F is said to be…


If X and (−1)X twain feel the similar distribution function F, defined on Rp, then F is said to be diagonally symmetric environing 0. Show that if F is diagonally symmetric environing 0, then for full ℓ ∈ Rp, ℓ ⊤X has a distribution function symmetric environing 0. This goods is connected to the multivariate median unbiasedness: If for full ℓ ∈ Rp, ℓ⊤(Tn − θ) has median 0, then Tn is multivariate median unprejudiced for θ. Verify (3.17). [Sen 1990]