Question

use the delta method theorem to obtain the asymptotic distribution of R

39. The California (CA) Department of Conservation assigns a "CA Redemption Value' (CRV) to recycled material which is due some reimbursement. The "commingled rate R is defined as the following ratio for the population of recycled material of any given type: R weight of CRV material / total weight. The sampling distribution of R is not easy to obtain. Consider the following approach. Let p the proportion of CRV bottles in the population of all recycled bottles. If p is the proportion in a random sample of n bottles, then, by the CLT va(p _ p) 4 Y ~ N(0, p(1-p)) as n- oo, Now if A and B are known conversion factors (i.e., A # of CRV bottles /lb and B-# of non-CRV bottles /lb) then we have p- AR/AR+B(1-R)]. This relationship suggests (solving for R in terms of p) that we estimate R by Use the delta method theorem to obtain the asymptotic distribution of R.

Answer 1