# 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.

• Do these "wild" estimates arise when the bootstrapped dataset samples very few cases, or the design matrix is very sparse so that the resulting logistic model has small sample bias, sometimes to such an extreme that the model is singular and point estimates are merely truncated GLM fitting routines that landed on the boundary? I wonder if those values are truly representative of the sampling distribution of the OR. Perhaps a more stable resampling based statistic would be the jackknife... – AdamO Dec 7 '17 at 20:36
• The jackknife will not give me what I need. I need the flexibility of the bootstrap (can handle clustered data and shows true volatility of variable selection methods, for example). I wouldn't label this a logistic model small sample problem but more of an infinite regression coefficient/Hauck-Donner effect. For example a bootstrap sample can leave out observations and result in an infinite estimate for a log odds ratio, which the MLE algorithm might see as a log odds ratio of 20 or 30. – Frank Harrell Dec 9 '17 at 13:40
• I wonder if your post is the same (essentially) as mine here. If so I'll close mine as duplicate. – AdamO Dec 12 '17 at 14:39
• No I think your post is about a different issue. – Frank Harrell Dec 13 '17 at 1:23