I need a little more help with this question:
Give an unbiased estimate of the variance of the estimator. (This may be compared to the value of the simpler alternative estimator.)
The answer to this question is 62.46, but I need to see a proof to understand how to calculate it myself.
Note - Below is the previous information(i.e answers) to help with the problem. Please do not provide me with answers or proofs to the questions below. I already have calculated those. I am only interested in seeing a proof of the answer above. I have no idea what a proof of this kind of question looks like and the textbook is unhelpful.
An unequal probability sample of size 3 is selected from a population of size 10 with replacement. The y-values of the selected units are listed along with their draw-by-draw selection probabilities: y1 = 3, p1 = 0.06; y2 = 10, p2 = 0.20; y3 =7, p3 =0.10.
The population total using the Hansen–Hurwitz estimator is 56.667
The variance of the estimator is 44.444
The population total using the Horvitz–Thompson estimator is:
Pi 1 = .1694, Pi 2 = .488, Pi 3 = .271, Population = 64.03
I need a little more help with this question: Give an unbiased estimate of the variance...
I need a little more help with this question: Give an unbiased estimate of the variance of the estimator using the Horvitz-Thompson estimator. (This may be compared to the value of the simpler alternative estimator.) The answer to this question is 62.46, but I need to see a proof of the variance of the estimator using the Horvitz-Thompson variance estimator to understand how to calculate it myself. I have included an image of the equation below: Note - Below is...
I need a little more help with this question: Give an unbiased estimate of the variance of the estimator. (This may be compared to the value of the simpler alternative estimator.) Here is the previous information to help with the problem. An unequal probability sample of size 3 is selected from a population of size 10 with replacement. The y-values of the selected units are listed along with their draw-by-draw selection probabilities: y1 = 3, p1 = 0.06; y2 =...