Let OCR and & : Rk Rd. We say that an estimator Tn : Xn Rd for (0) is regular if for every hR, we have h d Le under P n, 0+ + " (- (0++)) (In Tn with a probability measure Lo that does not depend on h. As a concrete example, let X1, , - the estimator Xn be i.i.d. with X ~ N(0, 0) and unknown 0 > 0. We consider - T n 2 ). n i=1 (a) Show that on is a consistent estimator for 0. (b) Show that on is a regular estimator for O and determine the asymptotic variance of Vo n). Hint: You need to use Le Cam's third Lemma. As an intermediate step, it is helpful to find the distribution of log dp n 0+h dpn {N(0,0): 0 > 0}. from the LAN property of the family of normal distributions