Question

1. Consider a ratio estimator h(1,6%) = 61/62, where the estimated variance- covariance for = | û lên] Covlên, ô2) vCov(@) = Covlê, ê2) Û @2]] Using the delta method, show that VẪhê, 2) = [1/8, -6,163 Cov(6) [ B.

consider a ratio estimator

by using delta method

Answer 1

considered Here , a natio estimator hl Estimated variance- coucriance vían los al vion can 10, od ] con conos s icoa) Now, for single parametes o, we know, if ô has variance of, then a continuous function of o, gio) has variance [g'(o).], where g'lo) is derivative with respect to o. Now for a parameters o, and of of its estimates oi and os has a variance covariance matras as the given matris in the question, then the gloi the covariance matrix of form has variance . doi ST var Ror los where or (0.02) saxi is a matrix with components of, and so ie. d 271 (sil where, dia a hros - so. a no (An here the continuous function is groen as heel bijos) So, ANI are the matrise calculate de Si co n10): veoma fas hig): 011027 a hle) = 102 Co2 o2032) - oz?

Hence, using della method, we can say - în con 08]. S T V Coulos ulo) sa ( 3 ) V LÊ ( )( = (a ) v row CÔ ) / (using (i) and (ii) (moreover, here we are using the estimates instead of parameters o, and oa, Entimates are a oa I