Note on Unitary Symmetry in Bootstrap Method

Note on Unitary Symmetry in Strong Interactions 951

The purpose cif this note is to investigate consequences of the three-dimensional unitary group (denoted as U 3 hereafter), which is a certain generalization of the usual isotopic space group. Though many authors1>'2J,aJ have examined this problem, our procedure is simpler and some new results have been obtained. Also, we can treat different schemes of U3 such as Sakata's1>' 2J or Gell-Mann's3>...

A note on approximate Bayesian bootstrap imputation

The approximate Bayesian bootstrap is suggested by Rubin & Schenker (1986) as a way of generating multiple imputations when the original sample can be regarded as independently and identically distributed and the response mechanism is ignorable. We investigate the finite sample properties of the variance estimator when the approximate Bayesian bootstrap method is used and show that the bias is ...

A Note on Cocycles of Unitary Representations

Given a unitary representation U of a locally compact abelian group G, we investigate the relationship between two cocycles a,, a2: Vax = a2+ b for some unitary operator V commuting with U and some coboundary b. A necessary and sufficient condition is given in terms of canonical-finite measures defined on G 1. These results are applied to the representation of Z defined by the shift of a statio...

Unitary Representations with Reeection Symmetry

On Bootstrap Tests of Symmetry About an Unknown Median.

It is important to examine the symmetry of an underlying distribution before applying some statistical procedures to a data set. For example, in the Zuni School District case, a formula originally developed by the Department of Education trimmed 5% of the data symmetrically from each end. The validity of this procedure was questioned at the hearing by Chief Justice Roberts. Most tests of symmet...