Abstract. In order to compute means, variances and higher moments of various partition statistics, one often has to study generating functions of the form P (x)F (x), where P (x) is the generating function for the number of partitions. In this paper, we show how asymptotic expansions can be obtained in a quasi-automatic way from expansions of F (x) around x = 1. Numerous examples from the liter...

The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra has been an outstanding issue. This original concept introduced long ago by Greenberg is the motivation for this investigation. We establish that a q-deformed algebra can be used to describe the statistics of particles (anyons) interpolating continuously between Bose and Fermi statistics, i...

Abstract We study linear subset regression in the context of high-dimensional overall model $y = \vartheta +\theta ' z + \epsilon $ with univariate response y and a d -vector random regressors , independent $\epsilon . Here, “high-dimensional” means that number available explanatory variables is much larger than n observations. consider simple submodels where regressed on set p given by $x M'z$...

Earl Lawrence * Statistical Sciences, Los Alamos National Laboratory P.O. Box 1663, MS F600 Los Alamos NM 87545 P: 505-665-0898, F: 505-667-4470, E: [email protected] George Michailidis Department of Statistics, University of Michigan 453 West Hall Ann Arbor MI 48109 P: 734-763-3498, F: 734-763-4676, E: [email protected] Vijayan N. Nair Department of Statistics, University of Michigan 277 West Hal...

Let F be a life distribution with survival function F = 1 F and 00 — finite mean y * j n F(x)dx. The scaled total time on test transform -1 F ( t ) — <P,,(t) = /n /F(x)dx/y was introduced by Barlow and Campo (1975) as a r U tool in the statistical analysis of life data. The properties IFR, IFRA, NBUE, DMRL and heavy-tailedness can be translated to properties of tp„(t). r We discuss the previous...

This paper presents a novel theory f o r learning generic prior models f r o m a set of observed natural images based o n a minimax entropy theory that the authors studied in modeling textures. W e start by studying the statistics of natural images including the scale invariant properties, then generic prior models were learnt t o duplicate the observed statistics. The learned Gibbs distributio...

Gene selection is an important issue in analyzing multiclass microarray data. Among many proposed selection methods, the traditional ANOVA F test statistic has been employed to identify informative genes for both class prediction (classification) and discovery problems. However, the F test statistic assumes an equal variance. This assumption may not be realistic for gene expression data. This p...

In 1978, Rivest, Adleman and Dertouzos asked for algebraic systems for which useful privacy homomorphisms exist. To date, the only acknownledged result is noise based encryption combined with bootstrapping. Before that, there were several failed attempts. We prove that fully homomorphic schemes are impossible for several algebraic structures. Then we develop a characterisation of all fully homo...