Let where with ci denoting regression constants, i = 1,...,n, and is known. Obtain the WLSE of the parameter θ when β = 1, 2, 0. The result is known as the ratio estimator. Show that when the...

Let

where

with c_i
denoting regression constants, i = 1,...,n, and

is known. Obtain the WLSE of the parameter θ when β = 1, 2, 0. The result is known as the ratio estimator.

Show that when the covariance matrix V_n
is diagonal, (2.4.8) may be expressed as (2.4.7). Furthermore, show that if all its non-null elements are equal, we have (2.4.4).