Which of the following characteristics is necessary for an estimator to be considered unbiased?

For an estimator to be considered unbiased, it is essential that the expected value of the estimator equals the parameter it is estimating. This means that if you were to take an infinite number of samples and calculate the estimator (for instance, the sample mean) for each sample, the average of those estimates would converge to the true value of the population parameter being estimated (such as the population mean).

This characteristic ensures that the estimator does not systematically overestimate or underestimate the parameter; instead, it centers around the true value on average, which is a fundamental requirement for unbiasedness. Consistency, finite variance, and normal distribution, while important properties of estimators, do not directly address the crucial aspect of unbiasedness. For instance, an estimator can be consistent (i.e., it converges in probability to the true parameter as the sample size increases) yet still be biased if its expected value does not align with the actual parameter value.