Exercise5.14 In Exercise2.22weestablishedthatthesample 100%-quantile Y() is the Mestimator correspondingto (,y) = (y)+ +(1)( y)+.

Exercise5.14 ∗ In Exercise2.22weestablishedthatthesample α · 100%-quantile Y(α) is the Mestimator correspondingto ρ(θ,y) = α(y−θ)+ +(1−α)(θ −y)+. Showthatundertherequired regularityconditions, Y(α) is aconsistentestimatorofa α ·100%-quantile F−1

θ0

(α) of thedistribution of Yi’swithatrue θ0 and finditsasymptoticdistribution.