Step 1: Understanding the Question
The question asks to identify the specific property of a statistical estimator where its average value (expected value) over all possible samples is equal to the true value of the population parameter it is trying to estimate.
Step 2: Detailed Explanation
Let's define the properties listed in the options:
Consistency: An estimator is consistent if it converges in probability to the true parameter value as the sample size increases.
Efficiency: This refers to the estimator having the smallest variance among all unbiased estimators. An efficient estimator is more precise.
Unbiasedness: An estimator \( \hat{\theta} \) is said to be unbiased for a parameter \( \theta \) if its expected value is equal to the true parameter, i.e., \( E(\hat{\theta}) = \theta \). This means the estimator does not systematically overestimate or underestimate the parameter.
Sufficiency: A sufficient statistic is one that captures all the information in the sample about the population parameter.
The condition given in the question, "its expected value equals the population parameter," directly matches the definition of unbiasedness.
Step 3: Final Answer
The property of an estimator that is satisfied if its expected value equals the population parameter is Unbiasedness.