5. Horvitz-Thompson (HT) estimator (a) (2 marks) Show that the HT estimator es tu/su is unbiased...
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 =...
To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with the finite variance σ 2 , we first take a random sample of size n . Then, we randomly draw one of n slips of paper numbered from 1 through n , and • if the number we draw is 2, 3, ··· , or n , we use as our estimator the...
To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with the nite variance 2, we rst take a random sample of size n. Then, we randomly draw one of n slips of paper numbered from 1 through n, and if the number we draw is 2, 3, , or n, we use as our estimator the mean of the random sample; otherwise, we...
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...
10.41] To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with the finite variance σ2, we first take a random sample of size n. Then, we randomly draw one of n slips of paper numbered from 1 through n, and if the number we draw is 2, 3, ..., orn, we use as our estimator the mean of the random sample; otherwise, we...
To show that an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with randomly draw o slips of paper numbered from 1 through n, and if the number we draw is 2, 3,.. .or n, we use as our estimator the mean of the random sample; otherwise, we use the estimate n2. Show that this estimation procedure is (a) consistent; (b) neither unbiased nor asymptotically...
To show that an estimator can be consistent without being unbiased or even asymptotically the finite variance σ, we first take a random sample of size n. Then we randomly draw one of n slips of paper numbered from 1 through n, and if the number we draw is 2, 3,.., or n, we use as our estimator the mean of the random sample; otherwise, we use the estimate n2. Show that this estimation procedure is (a) consistent; (b) neither...
For the population of N = 5 units of Exercise 3 of Chapter 2 (a) Compute directly the variance var (y) of the sample mean and the variance var( m ) of the sample median. (b) From each sample, compute the sample variance s 2 and the estimate var (y) of the variance of the sample mean. Show that the sample variance s 2 is unbiased for the √ finite-population variance σ 2 but that the sample standard deviation 2...
2. Biased and unbiased estimation for variance of Bernoulli variables A Bookmark this page 2 points possible (graded) Let X1, X, bed. Bernoull random variables, with unknown parameter PE (0,1). The aim of this exercise is to estimate the common variance of the X First, recall what Var (X) is for Bernoulli random variables. Var (X) - Let X, be the sample average of the Xi. X. - 3x Interested in finding an estimator for Var(X), and propose to use...