Sorry.
Some more comments.
(1) If you want an arbitrary sample size, you may need to write a function
to produce a simulated data set, for that given sample size.
Alternatively, you can use a random sample of size n, of an initial data
set, assuming the initial data set is relatively large.
(2) For each combination of n sample size and m% missing values, you may
need to compute your statistic, many (i.e. thousands of) times.
Then compute the mean and variance of your statistic.
(3) I have assumed that you want to start with a data.frame with no missing
values, and then set random subset(s) to missing values.
(4) Note that GAMs can have interaction terms.
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