The parametric bootstrap

Generally speaking, when we have a properly specified model, simulating from the model often provides reliable estimates even with smaller number of replicates than the non-parametric bootstrap. However, if the parametric model is mis-specified, the solution converges to the wrong distribution. Thus, when using the parametric bootstrap, the assumptions must hold.

We would like to show an application of the parametric bootstrap to show the properties of this method. Suppose that we have information that allow us to conclude that the two variables income and prestige in the dataset Prestige (package car) are drawn from a bivariate normal distribution – this is the model here to be assumed. We now estimate the mean and covariance from the empirical data and draw from the theoretical normal distribution with the corresponding parameter values of the empirical data:

## MASS needed for drawing random numbers from multivariate normal
library("MASS")
## parameters from empirical...