Robust Bootstrap Covariance Estimator I sometimes see particular bootstrap repetitions give "wild" regression coefficient estimates for one or more bootstrap resamples.  This occurs more often in binary logistic regression.  One or two wild parameter estimates can greatly distort the bootstrap covariance estimator that uses the sums of squares and cross-products of the $B \times p$ matrix of parameter estimates ($B$ = number of bootstraps, $p$ = number of parameters).
Is there a recommended way to robustify the covariance estimator based on bootstrap repetitions?  I don't want to use a method that changes the meaning of the covariance estimators, e.g., simple trimmed estimates would artificially reduce variances.
 A: I think you can just use robust estimator of covariance for each bootstrap estimation and it will work. This is not specific to your application.
There are a lot of different ways to have a robust covariance estimator. You can't avoid "artificially reduce variances" as you say because the "wild" estimates are consequence of a too large variance that you want to trim but you have to choose an estimator that trim the variance of outliers but do not trim the variance of inliers.
Among robust covariance estimators, one can use Minimum Covariance Determinant but this estimator suppose an elliptical density model on the data. Instead, I prefer to use M-estimators. For instance, in R, you can find such estimators rrcov or in robust package or you can code it yourself. And then, there is always a parameter that you have to tune (for instance, you say that you ignore the 5% of the data that are the "wilder" or something like that).
If you want a more precise answer, maybe you could give an example of a simulation or real dataset where what you speak of occurs.
