The correct answer is: A. Asymptotics generally give assurances about finite sample performance.
Asymptotics are used to study the behavior of a function as its argument approaches a certain value. In statistics, asymptotics are used to study the behavior of estimators as the sample size approaches infinity. However, asymptotics cannot be used to make inferences about the finite sample performance of an estimator.
The sample variance and the sample standard deviation are consistent estimators of the population variance and standard deviation, respectively. This means that as the sample size increases, the sample variance and sample standard deviation will converge to the population variance and standard deviation, respectively.
The sample mean is an unbiased estimator of the population mean. This means that the expected value of the sample mean is equal to the population mean.
Therefore, the correct answer is: A. Asymptotics generally give assurances about finite sample performance.