50,874 research outputs found
Three Dimensional Gauge Theory with Topological and Non-topological Mass: Hamiltonian and Lagrangian Analysis
Three dimensional (abelian) gauged massive Thirring model is bosonized in the
large fermion mass limit. A further integration of the gauge field results in a
non-local theory. A truncated version of that is the Maxwell Chern Simons (MCS)
theory with a conventional mass term or MCS Proca theory. This gauge invariant
theory is completely solved in the Hamiltonian and Lagrangian formalism, with
the spectra of the modes determined. Since the vector field constituting the
model is identified (via bosonization) to the fermion current, the charge
current algebra, including the Schwinger term is also computed in the MCS Proca
model.Comment: Eight pages, Latex, No figures
Small Area Shrinkage Estimation
The need for small area estimates is increasingly felt in both the public and
private sectors in order to formulate their strategic plans. It is now widely
recognized that direct small area survey estimates are highly unreliable owing
to large standard errors and coefficients of variation. The reason behind this
is that a survey is usually designed to achieve a specified level of accuracy
at a higher level of geography than that of small areas. Lack of additional
resources makes it almost imperative to use the same data to produce small area
estimates. For example, if a survey is designed to estimate per capita income
for a state, the same survey data need to be used to produce similar estimates
for counties, subcounties and census divisions within that state. Thus, by
necessity, small area estimation needs explicit, or at least implicit, use of
models to link these areas. Improved small area estimates are found by
"borrowing strength" from similar neighboring areas.Comment: Published in at http://dx.doi.org/10.1214/11-STS374 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Smoothed and Iterated Bootstrap Confidence Regions for Parameter Vectors
The construction of confidence regions for parameter vectors is a difficult
problem in the nonparametric setting, particularly when the sample size is not
large. The bootstrap has shown promise in solving this problem, but empirical
evidence often indicates that some bootstrap methods have difficulty in
maintaining the correct coverage probability, while other methods may be
unstable, often resulting in very large confidence regions. One way to improve
the performance of a bootstrap confidence region is to restrict the shape of
the region in such a way that the error term of an expansion is as small an
order as possible. To some extent, this can be achieved by using the bootstrap
to construct an ellipsoidal confidence region. This paper studies the effect of
using the smoothed and iterated bootstrap methods to construct an ellipsoidal
confidence region for a parameter vector. The smoothed estimate is based on a
multivariate kernel density estimator. This paper establishes a bandwidth
matrix for the smoothed bootstrap procedure that reduces the asymptotic
coverage error of the bootstrap percentile method ellipsoidal confidence
region. We also provide an analytical adjustment to the nominal level to reduce
the computational cost of the iterated bootstrap method. Simulations
demonstrate that the methods can be successfully applied in practice
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