Singh's theorem in the lattice case

The asymptotic behavior of the parametric bootstrap estimator of the sampling distribution of a maximum likelihood estimator is investigated in a simple lattice case, integer valued random variables whose distributions form an exponential family. The expected value of the bootstrap estimator is compared with an Edgeworth expansion, less the continuity correction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27029/1/0000017.pd

Bootstrapping least distance estimator in the multivariate regression model

The most popular estimation methods in multivariate linear regression are the multivariate least squares estimation and the multivariate least absolute estimation. Each method repeats its univariate estimation method p, the number of response variables, times. Although they are relatively easy to apply, they do not employ the relationship between response variables. This study considers the multivariate least distance estimator of Bai et al. (1990) that accounts for this relationship. We confirm its relative efficiency with respect to the multivariate least absolute estimator under the multivariate normal distribution and contaminated distribution. However, the asymptotic inference of the multivariate least distance estimator is shown to perform poorly in certain circumstances. We suggest the bootstrap method to infer the regression parameters and confirm its viability using Monte Carlo studies.

Singh's theorem in the lattice case

The asymptotic behavior of the parametric bootstrap estimator of the sampling distribution of a maximum likelihood estimator is investigated in a simple lattice case, integer valued random variables whose distributions form an exponential family. The expected value of the bootstrap estimator is compared with an Edgeworth expansion, less the continuity correction.bootstrap estimator Edgeworth expansions fractional part maximum likelihood estimator very weak expansions

Bootstrap confidence cones for directional data

International audienc