The correct answer is D. All of the mentioned.
Asymptotics are incredibly useful for simple statistical inference and approximations. They can be used to understand the behavior of estimators and test statistics as the sample size gets large. This can help us to make inferences about the population parameters with greater confidence.
Asymptotics often lead to nice understanding of procedures. For example, the central limit theorem tells us that the sampling distribution of the mean will be approximately normal as the sample size gets large. This means that we can use the normal distribution to make inferences about the population mean, even if the sample size is small.
An estimator is consistent if it converges to what you want to estimate. This means that as the sample size gets large, the estimator will get closer and closer to the true value of the parameter.
In conclusion, asymptotics are incredibly useful for simple statistical inference and approximations. They can be used to understand the behavior of estimators and test statistics as the sample size gets large. This can help us to make inferences about the population parameters with greater confidence.