An estimator is a function of random variables used for estimating a parameter. It can be thought of as the rule that creates an estimate. Which term matches?

An estimator is a function of random variables used for estimating a parameter. It can be thought of as the rule that creates an estimate. Which term matches?

• A. Estimator
• B. Statistic
• C. Parameter
• D. Variable

Answer: (A)

At the heart of this idea is the distinction between a rule and the result. An estimator is the rule or function that takes the observed data (random variables) and produces an estimate of a population parameter. It’s the method you apply to the data to form an estimate—for example, using the sample mean as the estimator of the population mean. A statistic, by contrast, is the actual numerical value you obtain after applying that rule to a particular sample; it is a concrete result, which can vary from sample to sample because the data vary. The parameter is the true, fixed value in the population that you’re trying to estimate, which you don’t know. A variable is a general quantity that can take on values, not a specific rule or resulting estimate. So the described concept—the function used to estimate a parameter—best matches the estimator.

At the heart of this idea is the distinction between a rule and the result. An estimator is the rule or function that takes the observed data (random variables) and produces an estimate of a population parameter. It’s the method you apply to the data to form an estimate—for example, using the sample mean as the estimator of the population mean.

A statistic, by contrast, is the actual numerical value you obtain after applying that rule to a particular sample; it is a concrete result, which can vary from sample to sample because the data vary. The parameter is the true, fixed value in the population that you’re trying to estimate, which you don’t know. A variable is a general quantity that can take on values, not a specific rule or resulting estimate.

So the described concept—the function used to estimate a parameter—best matches the estimator.