Let f(x) be the triangular density on [1, 1] defined by f(x) = (1 |x|)I{x [1, 1]} . Let P be the distribution

Let f(x) be the triangular density on [−1, 1] defined by f(x) = (1 − |x|)I{x ∈ [−1, 1]} .

Let Pθ be the distribution with density f(x−θ). Find the asymptotic behavior of H(Pθ0 , Pθ0+h) as h → 0, where H is the Hellinger distance. Compare your result with q.m.d. families.

Section 13.2