Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues

Details Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues

2009-06-11

arxiv.org/abs/0906.2128v1

Bernoulli 2009, Vol. 15, No. 2, 380-401

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ154 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ154

Bootstrap methods are widely used for distribution estimation, although in some problems they are applicable only with difficulty. A case in point is that of estimating the distributions of eigenvalue estimators, or of functions of those estimators, when one or more of the true eigenvalues are tied. The $m$-out-of-$n$ bootstrap can be used to deal with problems of this general type, but it is very sensitive to the choice of $m$. In this paper we propose a new approach, where a tie diagnostic is used to determine the locations of ties, and parameter estimates are adjusted accordingly. Our tie diagnostic is governed by a probability level, $\beta$, which in principle is an analogue of $m$ in the $m$-out-of-$n$ bootstrap. However, the tie-respecting bootstrap (TRB) is remarkably robust against the choice of $\beta$. This makes the TRB significantly more attractive than the $m$-out-of-$n$ bootstrap, where the value of $m$ has substantial influence on the final result. The TRB can be used very generally; for example, to test hypotheses about, or construct confidence regions for, the proportion of variability explained by a set of principal components. It is suitable for both finite-dimensional data and functional data.

Affiliated with

Also associated with

No associations

Rating

Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-516775