Homework Answers
The answer is:
If we have two unbiased estimators but one of the estimators has a large variance, it is basically useless. So a smaller variance is preferred for an unbiased estimator for it to be relatively efficient.
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If there are two unbiased estimators of a parameter, the one whose variance is A is...
Refer to Question 11 Figure, which shows the sampling distributions of two unbiased point estimators. Which...
Refer to Question 11 Figure, which shows the sampling distributions of two unbiased point estimators. Which of the following statements is correct? Question 11 Figure: Sampling distribution of & Sampling distribution Parameter e, is relatively more efficient than 6 b. e, is as efficient as e, e2 is relatively more efficient than 9,. d. All of the above.
(a) Are they unbiased estimators for µ? (b) Compute the MSE for all the 4 estimators. (c) Which one is the best estimat...
(a) Are they unbiased estimators for µ?
(b) Compute the MSE for all the 4 estimators.
(c) Which one is the best estimator for µ? Why.
PLEASE answer all parts, thanks
Let X1, X2, ..., X, be and i.i.d. sample from some distribution with mean y and variance o? Let us construct several estimators for . Let îi = X, iz = X1, A3 = (X1 + X2)/2, W = X1 + X2 (a) Are they unbiased estimators for ?...
B. Find the variance of each of the unbiased estimators θ1-2X and θ,-(n+1)/nX(n)
uniform distribution
B. Find the variance of each of the unbiased estimators θ1-2X and θ,-(n+1)/nX(n)
B. Find the variance of each of the unbiased estimators θ1-2X and θ,-(n+1)/nX(n)
Suppose ˆθ1 and ˆθ2 are two unbiased estimators for θ. (i) Is ˆθ3 = θˆ 1+θˆ...
Suppose ˆθ1 and ˆθ2 are two unbiased estimators for θ. (i) Is ˆθ3 = θˆ 1+θˆ 2 2 unbiased? (ii) Suppose V ar( ˆθ1) = V ar( ˆθ2) and that Cov( ˆθ1, ˆθ2) = 0 . Then is ˆθ3 more efficient than ˆθ1 and ˆθ2? (iii) Suppose that Cov( ˆθ1, ˆθ2) = 0 but V ar( ˆθ1) < V ar( ˆθ2). Intuitively, when is ˆθ3 less efficient than ˆθ1?
1) LetX,, ,X, be i.i.d. Uniform (0 , ) random variables for some > 0 (unknown). Which of the following estimators of0 are unbiased and which ones are biased? For each of the biased estimators...
1) LetX,, ,X, be i.i.d. Uniform (0 , ) random variables for some > 0 (unknown). Which of the following estimators of0 are unbiased and which ones are biased? For each of the biased estimators ofO, find the MSE. (a)2X, (b) the smallest order statistic, (e) the largest order statistic, (d) x, /2 ) For each of the unbiased estimators of 0 in the above problem, find the variance. Which unbiased estimator has the smallest variance? Find the relative efficiency...
[3] TRUE or FALSE: In the presence of autocorrelation, the OLS estimators remain unbiased but are...
[3] TRUE or FALSE: In the presence of autocorrelation, the OLS estimators remain unbiased but are no longer efficient. [4] TRUE or FALSE: In the presence of autocorrelation, the estimated OLS variances will be unbiased estimators of the correct OLS variances. [5] TRUE or FALSE: The core time series models are the regression or static model, the autoregressive model, the distributed lag model, and the autoregressive distributed lag model.
Mean and variance Answer can be one or multiple If an estimator is unbiased, then its...
Mean and variance
Answer can be one or multiple
If an estimator is unbiased, then its value is always the value of the parameter, its expected value is always the value of the parameter, O it variance is the same as the variance of the parameter.
Estimator properties: 6 Estimators properties 6.1 Exercise 1 In order to estimate the average number of...
Estimator properties:
6 Estimators properties 6.1 Exercise 1 In order to estimate the average number of hours that children spend watching tv, a Bernoulli sample of size n = 5 children was selected from a primary school. Let X be the variable that represents the hours spent watching tv, let E(X)-μ the parameter to estimate and var(X-σ2 the variance. Compare the following two proposed estimators Τι 1. Compare the two estimators for u on the basis of their bias 2....
8. Let X, X,, ... , X, be a rs from a distribution with mean u and variance o. Which of п these unbiased estimators has...
8. Let X, X,, ... , X, be a rs from a distribution with mean u and variance o. Which of п these unbiased estimators has the smallest variance? b) X с) X, а) 4X,-3х,
LetX1,...,X10 be a random sample from a population with meanμand variance σ2.Consider the following estimators for...
LetX1,...,X10 be a random sample from a population with meanμand variance σ2.Consider the following estimators for μ:ˆΘ1=(X1+···+X10)/10,ˆ Θ2=(3X1−2X5+ 3X10)/2. Are these estimators unbiased (i.e. is their expectation equal toμ)? A. Both estimators are unbiased. B. Both estimators are biased.C. Only the second is unbiased. D. Only the first is unbiased.E. Insufficient information.
Refer to Question 11 Figure, which shows the sampling distributions of two unbiased point estimators. Which of the following statements is correct? Question 11 Figure: Sampling distribution of & Sampling distribution Parameter e, is relatively more efficient than 6 b. e, is as efficient as e, e2 is relatively more efficient than 9,. d. All of the above.
(a) Are they unbiased estimators for µ?
(b) Compute the MSE for all the 4 estimators.
(c) Which one is the best estimator for µ? Why.
PLEASE answer all parts, thanks
Let X1, X2, ..., X, be and i.i.d. sample from some distribution with mean y and variance o? Let us construct several estimators for . Let îi = X, iz = X1, A3 = (X1 + X2)/2, W = X1 + X2 (a) Are they unbiased estimators for ?...
uniform distribution
B. Find the variance of each of the unbiased estimators θ1-2X and θ,-(n+1)/nX(n)
B. Find the variance of each of the unbiased estimators θ1-2X and θ,-(n+1)/nX(n)
1) LetX,, ,X, be i.i.d. Uniform (0 , ) random variables for some > 0 (unknown). Which of the following estimators of0 are unbiased and which ones are biased? For each of the biased estimators ofO, find the MSE. (a)2X, (b) the smallest order statistic, (e) the largest order statistic, (d) x, /2 ) For each of the unbiased estimators of 0 in the above problem, find the variance. Which unbiased estimator has the smallest variance? Find the relative efficiency...
[3] TRUE or FALSE: In the presence of autocorrelation, the OLS estimators remain unbiased but are no longer efficient. [4] TRUE or FALSE: In the presence of autocorrelation, the estimated OLS variances will be unbiased estimators of the correct OLS variances. [5] TRUE or FALSE: The core time series models are the regression or static model, the autoregressive model, the distributed lag model, and the autoregressive distributed lag model.
Mean and variance
Answer can be one or multiple
If an estimator is unbiased, then its value is always the value of the parameter, its expected value is always the value of the parameter, O it variance is the same as the variance of the parameter.
Estimator properties:
6 Estimators properties 6.1 Exercise 1 In order to estimate the average number of hours that children spend watching tv, a Bernoulli sample of size n = 5 children was selected from a primary school. Let X be the variable that represents the hours spent watching tv, let E(X)-μ the parameter to estimate and var(X-σ2 the variance. Compare the following two proposed estimators Τι 1. Compare the two estimators for u on the basis of their bias 2....
8. Let X, X,, ... , X, be a rs from a distribution with mean u and variance o. Which of п these unbiased estimators has the smallest variance? b) X с) X, а) 4X,-3х,
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