17,518 research outputs found
Saddlepoint approximation for Student's t-statistic with no moment conditions
A saddlepoint approximation of the Student's t-statistic was derived by
Daniels and Young [Biometrika 78 (1991) 169-179] under the very stringent
exponential moment condition that requires that the underlying density function
go down at least as fast as a Normal density in the tails. This is a severe
restriction on the approximation's applicability. In this paper we show that
this strong exponential moment restriction can be completely dispensed with,
that is, saddlepoint approximation of the Student's t-statistic remains valid
without any moment condition. This confirms the folklore that the Student's
t-statistic is robust against outliers. The saddlepoint approximation not only
provides a very accurate approximation for the Student's t-statistic, but it
also can be applied much more widely in statistical inference. As a result,
saddlepoint approximations should always be used whenever possible. Some
numerical work will be given to illustrate these points.Comment: Published at http://dx.doi.org/10.1214/009053604000000742 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Transmission statistics and focusing in single disordered samples
We show in microwave experiments and random matrix calculations that in
samples with a large number of channels the statistics of transmission for
different incident channels relative to the average transmission is determined
by a single parameter, the participation number of the eigenvalues of the
transmission matrix, M. Its inverse, M-1, is equal to the variance of relative
total transmission of the sample, while the contrast in maximal focusing is
equal to M. The distribution of relative total transmission changes from
Gaussian to negative exponential over the range in which M-1 changes from 0 to
1. This provides a framework for transmission and imaging in single samples.Comment: 9 pages, 4 figure
Supervised cross-modal factor analysis for multiple modal data classification
In this paper we study the problem of learning from multiple modal data for
purpose of document classification. In this problem, each document is composed
two different modals of data, i.e., an image and a text. Cross-modal factor
analysis (CFA) has been proposed to project the two different modals of data to
a shared data space, so that the classification of a image or a text can be
performed directly in this space. A disadvantage of CFA is that it has ignored
the supervision information. In this paper, we improve CFA by incorporating the
supervision information to represent and classify both image and text modals of
documents. We project both image and text data to a shared data space by factor
analysis, and then train a class label predictor in the shared space to use the
class label information. The factor analysis parameter and the predictor
parameter are learned jointly by solving one single objective function. With
this objective function, we minimize the distance between the projections of
image and text of the same document, and the classification error of the
projection measured by hinge loss function. The objective function is optimized
by an alternate optimization strategy in an iterative algorithm. Experiments in
two different multiple modal document data sets show the advantage of the
proposed algorithm over other CFA methods
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