Variance of Estimator: Learn How to Calculate

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In summary, the variance of an estimator is a measure of how spread out the values of the estimator are from the mean. It can be calculated using the formula Var(θ) = E[(θ - E(θ))^2] and is influenced by factors such as sample size, data distribution, and estimator bias. Calculating the variance is important to understand the reliability and accuracy of the estimator, and it can also be used in practice to compare different estimators and determine required sample sizes.
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trenekas
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Hi there. I would like to ask you one question about variance of estimator.

Suppose that [itex]Y_i=βX_i+ε_i[/itex] and β estimator is [itex]\bar{Y}[/itex] / [itex]\bar{X}[/itex].

I calculated mean of estimator. I am not sure if it's correct, but i got that its equal to n*β. But how about variance.
Any help would be appreciated!
 
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  • #2
It would help if you could back up one step and define your terms.
 
  • #3
I found a solution :) Thank you.
 

1. What is the variance of an estimator?

The variance of an estimator is a measure of how spread out the values of the estimator are from the mean. It tells us how much the estimates obtained from the estimator vary from one another. A smaller variance indicates that the estimator is more precise and provides more reliable estimates.

2. How is the variance of an estimator calculated?

The variance of an estimator can be calculated using the formula: Var(θ) = E[(θ - E(θ))^2]. This formula takes the expected value of the squared difference between the estimator θ and its expected value E(θ). In simpler terms, it measures the average squared difference between the estimator and its mean.

3. What factors can affect the variance of an estimator?

The variance of an estimator can be affected by various factors such as the sample size, the distribution of the data, and the bias of the estimator. A larger sample size generally leads to a smaller variance, while a biased estimator can have a larger variance. Additionally, the shape and spread of the data can also impact the variance of an estimator.

4. Why is it important to calculate the variance of an estimator?

Calculating the variance of an estimator is important because it helps us understand the reliability and accuracy of the estimator. A smaller variance indicates that the estimator is producing consistent and precise estimates, while a larger variance suggests that the estimates may vary significantly from one another and may not be as reliable.

5. How can we use the variance of an estimator in practice?

In practice, the variance of an estimator is often used to compare the performance of different estimators for a given problem. By calculating the variance of each estimator, we can determine which one is more precise and provides more accurate estimates. Additionally, the variance can also be used to determine the required sample size for an estimator to achieve a desired level of precision.

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