48,272 research outputs found
Estimation of fractal dimension for a class of Non-Gaussian stationary processes and fields
We present the asymptotic distribution theory for a class of increment-based
estimators of the fractal dimension of a random field of the form g{X(t)},
where g:R\to R is an unknown smooth function and X(t) is a real-valued
stationary Gaussian field on R^d, d=1 or 2, whose covariance function obeys a
power law at the origin. The relevant theoretical framework here is ``fixed
domain'' (or ``infill'') asymptotics. Surprisingly, the limit theory in this
non-Gaussian case is somewhat richer than in the Gaussian case (the latter is
recovered when g is affine), in part because estimators of the type considered
may have an asymptotic variance which is random in the limit. Broadly, when g
is smooth and nonaffine, three types of limit distributions can arise, types
(i), (ii) and (iii), say. Each type can be represented as a random integral.
More specifically, type (i) can be represented as the integral of a certain
random function with respect to Lebesgue measure; type (ii) can be represented
as the integral of a second random functio
Saddlepoint approximation for moment generating functions of truncated random variables
We consider the problem of approximating the moment generating function (MGF)
of a truncated random variable in terms of the MGF of the underlying (i.e.,
untruncated) random variable. The purpose of approximating the MGF is to enable
the application of saddlepoint approximations to certain distributions
determined by truncated random variables. Two important statistical
applications are the following: the approximation of certain multivariate
cumulative distribution functions; and the approximation of passage time
distributions in ion channel models which incorporate time interval omission.
We derive two types of representation for the MGF of a truncated random
variable. One of these representations is obtained by exponential tilting. The
second type of representation, which has two versions, is referred to as an
exponential convolution representation. Each representation motivates a
different approximation. It turns out that each of the three approximations is
extremely accurate in those cases ``to which it is suited.'' Moreover, there is
a simple rule of thumb for deciding which approximation to use in a given case,
and if this rule is followed, then our numerical and theoretical results
indicate that the resulting approximation will be extremely accurate.Comment: Published at http://dx.doi.org/10.1214/009053604000000689 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A data-based power transformation for compositional data
Compositional data analysis is carried out either by neglecting the
compositional constraint and applying standard multivariate data analysis, or
by transforming the data using the logs of the ratios of the components. In
this work we examine a more general transformation which includes both
approaches as special cases. It is a power transformation and involves a single
parameter, {\alpha}. The transformation has two equivalent versions. The first
is the stay-in-the-simplex version, which is the power transformation as
defined by Aitchison in 1986. The second version, which is a linear
transformation of the power transformation, is a Box-Cox type transformation.
We discuss a parametric way of estimating the value of {\alpha}, which is
maximization of its profile likelihood (assuming multivariate normality of the
transformed data) and the equivalence between the two versions is exhibited.
Other ways include maximization of the correct classification probability in
discriminant analysis and maximization of the pseudo R-squared (as defined by
Aitchison in 1986) in linear regression. We examine the relationship between
the {\alpha}-transformation, the raw data approach and the isometric log-ratio
transformation. Furthermore, we also define a suitable family of metrics
corresponding to the family of {\alpha}-transformation and consider the
corresponding family of Frechet means.Comment: Published in the proceddings of the 4th international workshop on
Compositional Data Analysis.
http://congress.cimne.com/codawork11/frontal/default.as
Thermomagnetic torques in polyatomic gases
The application of the Scott effect to the dynamics of galactic and stellar rotation is investigated. Efforts were also made to improve the sensitivity and stability of torque measurements and understand the microscopic mechanism that causes the Scott effect
Improved classification for compositional data using the -transformation
In compositional data analysis an observation is a vector containing
non-negative values, only the relative sizes of which are considered to be of
interest. Without loss of generality, a compositional vector can be taken to be
a vector of proportions that sum to one. Data of this type arise in many areas
including geology, archaeology, biology, economics and political science. In
this paper we investigate methods for classification of compositional data. Our
approach centres on the idea of using the -transformation to transform
the data and then to classify the transformed data via regularised discriminant
analysis and the k-nearest neighbours algorithm. Using the
-transformation generalises two rival approaches in compositional data
analysis, one (when ) that treats the data as though they were
Euclidean, ignoring the compositional constraint, and another (when )
that employs Aitchison's centred log-ratio transformation. A numerical study
with several real datasets shows that whether using or
gives better classification performance depends on the dataset, and moreover
that using an intermediate value of can sometimes give better
performance than using either 1 or 0.Comment: This is a 17-page preprint and has been accepted for publication at
the Journal of Classificatio
Studies on the bit rate requirements for a HDTV format with 1920 1080 pixel resolution, progressive scanning at 50 Hz frame rate targeting large flat panel displays
This paper considers the potential for an HDTV delivery format with 1920 times 1080 pixels progressive scanning and 50 frames per second in broadcast applications. The paper discusses the difficulties in characterizing the display to be assumed for reception. It elaborates on the required bit rate of the 1080p/50 format when critical content is coded in MPEG-4 H.264 AVC Part 10 and subjectively viewed on a large, flat panel display with 1920 times 1080 pixel resolution. The paper describes the initial subjective quality evaluations that have been made in these conditions. The results of these initial tests suggest that the required bit-rate for a 1080p/50 HDTV signal in emission could be kept equal or lower than that of 2nd generation HDTV formats, to achieve equal or better image qualit
Implications of microwave spectroscopy for the water-vapor content of the Venus atmosphere
Brightness temperature spectra of Venus computed to determine amount of water vapor in lower atmospher
Mobility of Dislocations in Aluminum
The velocities of individual dislocations of edge and mixed types in pure aluminum single crystals were determined as a function of appliedâresolved shear stress and temperature. The dislocation velocities were determined from measurements of the displacements of individual dislocations produced by stress pulses of known duration. The BergâBarrett xâray technique was employed to observe the dislocations, and stress pulses of 15 to 108 ÎŒsec duration were applied by propagating torsional waves along the axes of [111]âoriented cylindrical crystals. Resolved shear stresses up to 16Ă10^6 dynesâcm^2 were applied at temperatures ranging from â150° to +70°C, and dislocation velocities were found to vary from 10 to 2800 cmâsec over these ranges of stress and temperature. The experimental conditions were such that the dislocation velocities were not significantly influenced by impurities, dislocation curvature, dislocationâdislocation interactions, or longârange internal stress fields in the crystals. The velocity of dislocations is found to be linearly proportional to the appliedâresolved shear stress, and to decrease with increasing temperature. Qualitative comparison of these results with existing theories leads to the conclusion that the mobility of individual dislocations in pure aluminum is governed by dislocationâphonon interactions. The phononâviscosity theory of dislocation mobility can be brought into agreement with the experimental results by reasonable choices of the values of certain constants appearing in the theory
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