I have a question regarding the definiton of estimators. In the german wikipedia it says that the distribution is determined by g($X_1,...,X_n$) where by g is the estimator function and $X_1,..X_n$ are the observed random variables, and g is evaluated for all possible samples.
Now my question is if the distribution of the estimator is evaluated for a fixed n, i.e. does each sample size has its own estimator distribution? Or is the distribution constructed for variable n?
Furtheron I am interested in the following: If I have a dataset of around 200 observations given, and I want to construct the distribution of an estimator for different sample sizes, is it recommended to use sampling without replacement or with replacement (i.e. bootstrapping)? The data is normally distributed, and the estimator to be calculated is the estimator for the t-test.