1,387 research outputs found
Using Java Technologies in Statistics Applications Data Analysis Graphic Generator
This paper proposes an idea for building a Java Application Programming Interface (API) that allows generating statistics graphics used in Data Analysis. The core of this API is a Java 2D library, and some classes which implement the 2D geometric transformations. The classes are small, fast, easy to use and can be integrated into your projects, and are completely written in pure Java. It allows users to easily develop and deploy sophisticated reports across any platform.Java API, Data Analysis, Graphics
Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression
Concentration inequalities form an essential toolkit in the study of high
dimensional (HD) statistical methods. Most of the relevant statistics
literature in this regard is based on sub-Gaussian or sub-exponential tail
assumptions. In this paper, we first bring together various probabilistic
inequalities for sums of independent random variables under much weaker
exponential type (namely sub-Weibull) tail assumptions. These results extract a
part sub-Gaussian tail behavior in finite samples, matching the asymptotics
governed by the central limit theorem, and are compactly represented in terms
of a new Orlicz quasi-norm - the Generalized Bernstein-Orlicz norm - that
typifies such tail behaviors.
We illustrate the usefulness of these inequalities through the analysis of
four fundamental problems in HD statistics. In the first two problems, we study
the rate of convergence of the sample covariance matrix in terms of the maximum
elementwise norm and the maximum k-sub-matrix operator norm which are key
quantities of interest in bootstrap, HD covariance matrix estimation and HD
inference. The third example concerns the restricted eigenvalue condition,
required in HD linear regression, which we verify for all sub-Weibull random
vectors through a unified analysis, and also prove a more general result
related to restricted strong convexity in the process. In the final example, we
consider the Lasso estimator for linear regression and establish its rate of
convergence under much weaker than usual tail assumptions (on the errors as
well as the covariates), while also allowing for misspecified models and both
fixed and random design. To our knowledge, these are the first such results for
Lasso obtained in this generality. The common feature in all our results over
all the examples is that the convergence rates under most exponential tails
match the usual ones under sub-Gaussian assumptions.Comment: 64 pages; Revised version (discussions added and some results
modified in Section 4, minor changes made throughout
Normal approximation for nonlinear statistics using a concentration inequality approach
Let be a general sampling statistic that can be written as a linear
statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds
for are obtained. The bounds are the best possible for many known
statistics. Applications to U-statistics, multisample U-statistics,
L-statistics, random sums and functions of nonlinear statistics are discussed.Comment: Published at http://dx.doi.org/10.3150/07-BEJ5164 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Coalescent tree based functional representations for some Feynman-Kac particle models
We design a theoretic tree-based functional representation of a class of
Feynman-Kac particle distributions, including an extension of the Wick product
formula to interacting particle systems. These weak expansions rely on an
original combinatorial, and permutation group analysis of a special class of
forests. They provide refined non asymptotic propagation of chaos type
properties, as well as sharp \LL\_p-mean error bounds, and laws of large
numbers for -statistics. Applications to particle interpretations of the top
eigenvalues, and the ground states of Schr\"{o}dinger semigroups are also
discussed
Cram\'{e}r-type moderate deviations for Studentized two-sample -statistics with applications
Two-sample -statistics are widely used in a broad range of applications,
including those in the fields of biostatistics and econometrics. In this paper,
we establish sharp Cram\'{e}r-type moderate deviation theorems for Studentized
two-sample -statistics in a general framework, including the two-sample
-statistic and Studentized Mann-Whitney test statistic as prototypical
examples. In particular, a refined moderate deviation theorem with second-order
accuracy is established for the two-sample -statistic. These results extend
the applicability of the existing statistical methodologies from the one-sample
-statistic to more general nonlinear statistics. Applications to two-sample
large-scale multiple testing problems with false discovery rate control and the
regularized bootstrap method are also discussed.Comment: Published at http://dx.doi.org/10.1214/15-AOS1375 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Spatio-temporal statistics : applications in epidemiology, veterinary medicine and ecology
Not available
Effect of Polydispersity and Anisotropy in Colloidal and Protein Solutions: an Integral Equation Approach
Application of integral equation theory to complex fluids is reviewed, with
particular emphasis to the effects of polydispersity and anisotropy on their
structural and thermodynamic properties. Both analytical and numerical
solutions of integral equations are discussed within the context of a set of
minimal potential models that have been widely used in the literature. While
other popular theoretical tools, such as numerical simulations and density
functional theory, are superior for quantitative and accurate predictions, we
argue that integral equation theory still provides, as in simple fluids, an
invaluable technique that is able to capture the main essential features of a
complex system, at a much lower computational cost. In addition, it can provide
a detailed description of the angular dependence in arbitrary frame, unlike
numerical simulations where this information is frequently hampered by
insufficient statistics. Applications to colloidal mixtures, globular proteins
and patchy colloids are discussed, within a unified framework.Comment: 17 pages, 7 figures, to appear in Interdiscip. Sci. Comput. Life Sci.
(2011), special issue dedicated to Prof. Lesser Blu
Lecture 04: Spatial Statistics Applications of HRL, TRL, and Mixed Precision
As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the smaller scales of the past because we could afford to do so. We present innovations that allow to approach lin-log complexity in storage and operation count in many important algorithmic kernels and thus create an opportunity for full applications with optimal scalability
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