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To show that an estimator can be consistent without being unbiased or even asymptotically unbiased, consider...
To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider 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...
To show that an estimator can be consistent without being unbiased or even asymptotically the finite...
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...
To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider 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 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...
10.41] To show an estimator can be consistent without being unbiased or even asymptotically unbiased, consider...
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...
Find a consistent estimator of µ 2 , where E(Y ) = µ is the population mean and Y¯ n is the sample mean. 2 If E(Y 2 ) =...
Find a consistent estimator of µ 2 , where E(Y ) = µ is the
population mean and Y¯ n is the sample mean. 2 If E(Y 2 ) = µ 0 2
then prove that 1 n Pn i=1 Y 2 i is an consistent estimator of µ 0
2 3 We define σ 2 = µ 0 2 − µ 2 . Show that S 2 n = 1 n Pn i=1 Y 2
i − Y¯ 2...
6. In Problem 1, show that θ2 is a consistent estimator for θ. Deduce that Y(n) is a consistent e...
Please answer as neatly as possible.
Much thanks in advance!
Question 1:
6. In Problem 1, show that θ2 is a consistent estimator for θ. Deduce that Y(n) is a consistent estimator for θ and also asyınpt○tically unbiased estimator for θ. 1. Let Yi, ½, . . . ,y, denote a random sample from an uniform distribution on the interval (0,0). We have seen that (1) and 62 Ym are unbiased estimators for 0. Find the efficiency of 6 relative...
5. Horvitz-Thompson (HT) estimator (a) (2 marks) Show that the HT estimator es tu/su is unbiased...
5. Horvitz-Thompson (HT) estimator (a) (2 marks) Show that the HT estimator es tu/su is unbiased for the population total. Clearly define any notation used. (b) (1 mark) The variance of the HT estimator is Var(ār(s)) = () Give the HT estimate of the variance based on the sample, S. (c) (1 mark) Suppose we sample with replacement where probability of selecting unit u is pu. Derive the inclusion probability for unit. (d) A sample (n = 6) was randomly...
Could you please give detailed steps? Thanks! Consider a random sample from the Poisson(0) distribution (e.g....
Could you please give detailed
steps? Thanks!
Consider a random sample from the Poisson(0) distribution (e.g. this setup could apply to the number of arrests example from class) You may take it as given that if X ~Poisson(0) then E[X_ θ)41-30" +θ (rememeber this is this is the 4th central moment or one of the definitions of kuutosis 3- (this is another commonly used definition of the kurtosis) (no need to show any of these) a. You wish to estimate...
QUESTION 21 If we change a 90% confidence interval estimate to a 99% confidence interval estimate...
QUESTION 21 If we change a 90% confidence interval estimate to a 99% confidence interval estimate while holding sample size constant, we can expect a. the width of the confidence interval to increase. b. the width of the confidence interval to decrease. c. the width of the confidence interval to remain the same. d. the sample size to increase. QUESTION 22 Which one of the following is a correct statement about the probability distribution of a t random variable? a....
Stat 5644 Spring 2019 Homework 4 Due 3/20 Problem :UMVUE via Rao-Blackwell, Lehmann-Scheffe, and ...
Stat 5644 Spring 2019 Homework 4 Due 3/20 Problem :UMVUE via Rao-Blackwell, Lehmann-Scheffe, and Basu theorems This problem is on the estimation of a reliability function. Let Xi, , x, be IID from N(μ, σ2). Let Φ(-) be the c.d.f. of the standard normal distribution. Assume that σ2-of is known, for now. It is of interest to estimate the reliability number σο for some c, with )-1-(). c is called cut of point in reliability (a) Give, without any proof,...
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...
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...
Find a consistent estimator of µ 2 , where E(Y ) = µ is the
population mean and Y¯ n is the sample mean. 2 If E(Y 2 ) = µ 0 2
then prove that 1 n Pn i=1 Y 2 i is an consistent estimator of µ 0
2 3 We define σ 2 = µ 0 2 − µ 2 . Show that S 2 n = 1 n Pn i=1 Y 2
i − Y¯ 2...
Please answer as neatly as possible.
Much thanks in advance!
Question 1:
6. In Problem 1, show that θ2 is a consistent estimator for θ. Deduce that Y(n) is a consistent estimator for θ and also asyınpt○tically unbiased estimator for θ. 1. Let Yi, ½, . . . ,y, denote a random sample from an uniform distribution on the interval (0,0). We have seen that (1) and 62 Ym are unbiased estimators for 0. Find the efficiency of 6 relative...
5. Horvitz-Thompson (HT) estimator (a) (2 marks) Show that the HT estimator es tu/su is unbiased for the population total. Clearly define any notation used. (b) (1 mark) The variance of the HT estimator is Var(ār(s)) = () Give the HT estimate of the variance based on the sample, S. (c) (1 mark) Suppose we sample with replacement where probability of selecting unit u is pu. Derive the inclusion probability for unit. (d) A sample (n = 6) was randomly...
Could you please give detailed
steps? Thanks!
Consider a random sample from the Poisson(0) distribution (e.g. this setup could apply to the number of arrests example from class) You may take it as given that if X ~Poisson(0) then E[X_ θ)41-30" +θ (rememeber this is this is the 4th central moment or one of the definitions of kuutosis 3- (this is another commonly used definition of the kurtosis) (no need to show any of these) a. You wish to estimate...
Stat 5644 Spring 2019 Homework 4 Due 3/20 Problem :UMVUE via Rao-Blackwell, Lehmann-Scheffe, and Basu theorems This problem is on the estimation of a reliability function. Let Xi, , x, be IID from N(μ, σ2). Let Φ(-) be the c.d.f. of the standard normal distribution. Assume that σ2-of is known, for now. It is of interest to estimate the reliability number σο for some c, with )-1-(). c is called cut of point in reliability (a) Give, without any proof,...
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