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