Estimating bias with bootstrap

Previously, the standard error was used as a measure of the accuracy of an estimator . We now want to look at the bias, the difference of the estimator and the parameters to be estimated the population – we want to look at systematic distortions of the estimator .

The reasons for bias in the data can be very different: systematic errors in registers, poor sampling design, heavy earners not reported, outliers, robust estimates of sampling means or totals in complex sampling designs, and so on.

The bias of is the deviation from the actual parameter of the population, that is, . Since is generally unknown, the bias can usually only be expressed using resampling. In the following, we only concentrate on this mathematical bias and do not consider any other kind of bias (such as systematic bias from data collection).

For the estimation of the bias, independent bootstrap samples, , are drawn, see Efron and Tibshirani (1993), and the bootstrap replications estimated...