Title: Speed-up of bootstrap computation of the covariance matrix of MLEs from incomplete data
Authors: Masahiro Kuroda - Okayama University of Science (Japan) [presenting]
Yuichi Mori - Okayama university of Science (Japan)
Abstract: The bootstrap is a most useful method to compute the covariance matrix of maximum likelihood estimates (MLEs) of parameters given a statistical model. In the bootstrap computation, we generate a bootstrap sample by randomly sampling with replacement from observed data and compute the MLEs using this sample. After repeating the procedure $B$ times, we can obtain the covariance matrix of the MLEs from the $B$ MLEs. When applying the bootstrap to incomplete data, we require to add an iterative computation step of finding MLEs to the bootstrap procedure. The EM algorithm is used in the MLE computation step and is applied to each of $B$ bootstrap samples. Then the bootstrap computation for incomplete data takes long computation time due to the slow convergence of the EM algorithm. In order to reduce the bootstrap computation cost, we provide a simple acceleration algorithm for speeding up the convergence of the EM algorithm. Numerical experiments examine the performance of the speed-up of the bootstrap computation using the accelerated EM algorithm for incomplete data.