Consider the Laplace distribution function: f(x) = (1/2)e −|x−θ| , x ∈ R. What is the BLUE of θ ? Verify whether or not C1, C2, or C3 holds. Consider the sample median X˜ n = T(Fn) = inf{x : Fn(x) ≥...

Consider the Laplace distribution function: f(x) = (1/2)e −|x−θ| , x ∈ R. What is the BLUE of θ ? Verify whether or not C1, C2, or C3 holds.

Consider the sample median X˜ n = T(Fn) = inf{x : Fn(x) ≥ 1/2} = F −1 n (0.5). thus, T(F) = F −1 (0.5) is the population counterpart of X˜ n. Is T(Fn) first-order Hadamard differentiable?