Let X1, . . . , Xn be i.i.d. with cdf F and pdf f . For any 0 < p < 1, let νp be such that F(νp) = p. Suppose that f (νp) > 0. Show that for any sequence m = mn such that m/n = p + o(n

−1/2), we have

√

n{X(m) − νp} −→d N(0, σ2 p), where X(i) is the ith order statistic, and σ2 p

= p(1 − p)/f 2(νp).