What is the difference between finite and infinite samples?

[Phuc Nguyen]

Today I faced a term "finite samples" in reading Borusyak (2021)'s work:

We conclude the section by providing simulation evidence that the efficiency gains from using our estimator are sizable, that its sensitivity to some parallel trend vio- lations is no larger than that of the alternatives, and that our inference tools perform well in finite samples

I did a search about the "finite sample" and "infinite sample"

Sampling from an infinite population is handled by regarding the population as represented by a distribution. ... A random sample from an infinite population is therefore considered as a random sample from a distribution

It seems to me that regarding "finite sample", we randomly choose a sample in a population and analyze this population and draw a conclusion for a population, and in an "infinite sample", we test for the whole population data to draw a conclusion for the population, is it correct?

[Jackson Monroe]

Your question is not directly related to Stata, but I'll answer anyway.

"Finite sample performance" has to do with the idea that many statistical methods are evaluated asymptotically, how they perform when the amount of data goes to infinity. Are they consistent (eventually converging to the correct value), are they efficient (converging as quickly as possible), etc.

Good asymptotic properties do not guarantee that using the method with real data, which is finite by definition, yields good results. When the authors speak of finite sample performance this is the distinction they are drawing. "We did some simulations and it works well in practice, even when there isn't much data."

[Carlo Lazzaro]

Phuc:
Chapter 3.2 of the valuable https://www.stata.com/bookstore/envi...s-using-stata/ covers this issue about the properties of estimators.

[Phuc Nguyen]

Your question is not directly related to Stata, but I'll answer anyway.

"Finite sample performance" has to do with the idea that many statistical methods are evaluated asymptotically, how they perform when the amount of data goes to infinity. Are they consistent (eventually converging to the correct value), are they efficient (converging as quickly as possible), etc.

Good asymptotic properties do not guarantee that using the method with real data, which is finite by definition, yields good results. When the authors speak of finite sample performance this is the distinction they are drawing. "We did some simulations and it works well in practice, even when there isn't much data."

It makes clear sense to me, thanks Jackson Monroe