ABSTRACT
Noting that n evaluated at f[Z N] equals e? and that dTl (£[ZN ])jdZ N equals ce?)2 and ignoring the remainder term R~· 1 since it will be negligible in a neighborhood of f[ZN], which equals 1/8?, one obtains
With a minor amount of manipulation, one then obtains
In the lognormal case, the GLC solves
o v 2rra2 2a
defined
(5)
In this case, both ;(q; ft, o-2) and Q(q; ft, a 2 ) are only defined numerically. For a specific q, conditional on some estimates rn and 52 , one can solve the quantile equation (5) numerically and then the GLC equation (4). To apply the delta method, one would have to use Leibniz's rule to find the effect of ehanges in M and S2 on the asymptotie distribution of Q(q; ft, a 2 ) at q. A similar analysis could also be performed to find the asymptotic distribution of £(q; ft, o-2). As one can see, except in a few simple cases, the teehnical demands can increase when parametric methods arc used because the quantiles are often only defined implicitly and the LCs and GLCs can typically only be calculated numerically, in the continuous ease. Moreover, the
calculationsrequiredtocharacterizetheasymptoticdistributionofthepointwisE'estimatorofeithertheLCortheGLCcanbelongandtedious.This,ofcourse,isnot themaindrawbackofthisapproach.
