Efficient Bootstrap Simulation in Linear Regression

Abstract

Two basic sources of errors are associated to the use of bootstrap methods: one is derived from the fact that the true distribution is substituted by a suitable estimate, and the other is simulation errors. Some techniques to reduce or quantify these errors such as importance sampling or antithetic variates are adapted from classical Monte Carlo swindles, whereas others such as the centered and the balanced bootstrap are more specific.

The classical importance sampling estimate is well-suited for variance reduction in rare event applications. It fails in many other applications. The ratio and regression estimates, well-known in sampling theory, succeed in many of these cases.

In our work we have done various simulations in linear models to determine the needed number of the bootstrap replications.