I'm trying to approximate by bootstrap the standard error of a regression-type estimator for which the asymptotic distribution is difficult to calculate. I have a 0-1 coded dummy variable in the model that equals one in only a few cases. In some iterations, none of the observations sampled include the dummy variable valued at one, so the corresponding column of the data matrix contains all zeroes, and the covariance matrix for the sampled data is singular (because the model also includes an intercept). As a result, I cannot estimate the value of the parameter.
I'm trying to figure out a way around this problem. Won't removing the regressor from the estimated model on these iterations potentially introduce a bias in the remaining coefficients and overstate their standard errors?
Any suggestions are appreciated!