I'm trying to implement the "Free Step-Down Resampling Method" described by Westfall and Young in "Resampling-Based Multiple Testing" (algorithm ~2.8 in the text). My goal is to perform a multivariate linear regression.
So, I have an error estimate (from the original sample) like this (using OLS):
$\epsilon = Y - (\beta_0 + \beta_1X_1 + \beta_2X_2 + \dots \beta_pX_p)$
[BTW, $X_1 \dots X_p$ are dummy variables.]
In order to resample ($i$ times), I have to do:
$Y_i^* = \epsilon_i^*$
where $\epsilon_i^*$ is a with replacement sample from the original $\epsilon$.
Here is the problem:
In my dataset, responses (rows) are clustered (data come from related individuals); so, I would usually have applied Huber-White estimators to account for correlations in OLS-based linear regressions.
I don't know how to proceed here... Should Huber-White estimators be used? If so, how?
Apologies if my question is too simple, but I'm new in resampling methods... I guess the answer is simple, too. Suggestions are welcome.