Question

An unbiased estimator A. always captures the true population value of the parameter. B. has no variation due to resampling. C. is necessarily the best estimator, i.e., it achieves the minimum variance. D. captures the true population value of the parameter on average, i.e., the mean of its sampling distribution is the truth. E. cannot be calculated.

Answer 1

C. is necessarily the best estimator, i.e., it achieves the minimum variance.

D. captures the true population value of the parameter on average, i.e., the mean of its sampling distribution is the truth.

Explanation:

In statistics, If your data is not an overestimate or underestimate of a population parameter, then your statistic is said to be unbiased.

When an accurate statistic is used to approximate a population parameter it is known as an Unbiased estimator. “Accurate” in this context means it’s neither an overestimate nor an underestimate.

Mathematically, an estimator is said to be unbiased if: <Ô> = Ø

The above equation means that when the sample mean equals the population mean then it is unbiased estimator.

However, If an overestimate or underestimate occurs, the mean of the difference is called a “bias.”

Answer 2

Options A, C and D are all correct.

An unbiased estimator

- always captures the true population value of the parameter

- is necessarily the best estimator, i.e., it achieves the minimum variance.

- captures the true population value of the parameter on average, i.e., the mean of its sampling distribution is the truth.

Explanation:

The bias in an estimate is defined as the difference between the true value and the estimated value.

When there is no difference between the estimated and true value, the estimate is said to be unbiased.

An unbiased estimator can obtain a population parameter perfectly from sample statistic.

So, just like option A, the unbiased estimator always captures the population parameter.

It is usually obtained from a distribution of different samples of the dataset. Different samples have sample means that are close in value to each other, the unbiased estimator obtains the population mean by taking an average of all the sample means from all the different samples (option D) and has the minimum value of variance in distribution of sample means (option C)

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