5,534 research outputs found
Testing for Bivariate Spherical Symmetry
An omnibus test for spherical symmetry in R2 is proposed, employing localized empirical likelihood. The thus obtained test statistic is distri- bution-free under the null hypothesis. The asymptotic null distribution is established and critical values for typical sample sizes, as well as the asymptotic ones, are presented. In a simulation study, the good perfor- mance of the test is demonstrated. Furthermore, a real data example is presented.Asymptotic distribution;distribution-free;empirical like- lihood;hypothesis test;spherical symmetry.
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Some contributions to the analysis of skew data on the line and circle
In the first part of this thesis we consider the skew-normal class of distributions on the line and its limiting general half-normal distribution. Inferential procedures based on the methods of moments and maximum likelihood are developed and their performance assessed using simulation. Data on the strength of glass fibre and the body fat of elite athletes are used to illustrate some of the inferential issues raised. The second part of the thesis is devoted to a consideration of the analysis of skew circular data. First, we derive the large-sample distribution of certain key circular statistics and show how this result provides a basis for inference for the corresponding population measures. Next, tests for circular reflective symmetry about an unknown central direction are investigated. A large-sample test and computer intensive variants of it are developed, and their operating characteristics explored both theoretically and empirically. Subsequently, we consider tests for circular reflective symmetry about a known or specified median axis. Two new procedures are developed for testing for symmetry about a known median axis against skew alternatives, and their operating characteristics compared in a simulation experiment with those of the circular analogues of three linear tests. On the basis of the results obtained from the latter, a simple testing strategy is identified. The performance of the tests against rotation alternatives is also investigated. Throughout, the use of the various tests of symmetry is illustrated using a wide range of circular data sets. Finally, we propose the wrapped skew-normal distribution on the circle as a potential model for circular data. The distribution’s fundamental properties are presented and inference based on the methods of moments and maximum likelihood is explored. Tests for limiting cases of the class are proposed, and a potential use of the distribution is illustrated in the mixture based modelling of data on bird migration
Tapering promotes propriety for Fourier transforms of real-valued time series
We examine Fourier transforms of real-valued stationary time series from the point of view of the statistical propriety. Processes with a large dynamic range spectrum have transforms that are very significantly improper for some frequencies; the real and imaginary parts can be highly correlated, and the periodogram will not have the standard chi-square distribution at these frequencies, nor have two degrees of freedom. Use of a taper reduces impropriety to just frequencies close to zero and Nyquist only, and frequency ranges where the propriety breaks down can be quite accurately and easily predicted by half the autocorrelation width of |H * H(2f)|, denoted by c, where H(f) is the Fourier transform of the taper and * denotes convolution. For vector time series we derive an improved distributional approximation for minus twice the log of the generalized likelihood ratio test statistic for testing for propriety of the Fourier transform at any frequency, and compare frequency range cutoffs for propriety determined by the hypothesis test with those determined by c
Detecting simultaneous variant intervals in aligned sequences
Given a set of aligned sequences of independent noisy observations, we are
concerned with detecting intervals where the mean values of the observations
change simultaneously in a subset of the sequences. The intervals of changed
means are typically short relative to the length of the sequences, the subset
where the change occurs, the "carriers," can be relatively small, and the sizes
of the changes can vary from one sequence to another. This problem is motivated
by the scientific problem of detecting inherited copy number variants in
aligned DNA samples. We suggest a statistic based on the assumption that for
any given interval of changed means there is a given fraction of samples that
carry the change. We derive an analytic approximation for the false positive
error probability of a scan, which is shown by simulations to be reasonably
accurate. We show that the new method usually improves on methods that analyze
a single sample at a time and on our earlier multi-sample method, which is most
efficient when the carriers form a large fraction of the set of sequences. The
proposed procedure is also shown to be robust with respect to the assumed
fraction of carriers of the changes.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS400 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Non-null Distribution of The Likelihood Ratio Statistic for Testing Multisample Compound Symmetry
The non-null distribution of the modified likelihood ratio test statistic Λ∗ for testing multisample compound symmetry of q multivariate Gaussian models is derived. The non-null moments of Λ∗ are obtained in terms of Lauricella's hypergeometric function. The non-null distribution is expressed in terms of H-function.
Non-null Distribution of The Likelihood Ratio Statistic for Testing Multisample Compound Symmetry
The non-null distribution of the modified likelihood ratio test statistic Λ∗ for testing multisample compound symmetry of q multivariate Gaussian models is derived. The non-null moments of Λ∗ are obtained in terms of Lauricella's hypergeometric function. The non-null distribution is expressed in terms of H-function. 
The host galaxies of luminous radio-quiet quasars
We present the results of a deep K-band imaging study which reveals the host
galaxies around a sample of luminous radio-quiet quasars. The K-band images,
obtained at UKIRT, are of sufficient quality to allow accurate modelling of the
underlying host galaxy. Initially, the basic structure of the hosts is revealed
using a modified Clean deconvolution routine optimised for this analysis. 2 of
the 14 quasars are shown to have host galaxies with violently disturbed
morphologies which cannot be modelled by smooth elliptical profiles. For the
remainder of our sample, 2D models of the host and nuclear component are fitted
to the images using the chi-squared statistic to determine goodness of fit.
Host galaxies are detected around all of the quasars. The reliability of the
modelling is extensively tested, and we find the host luminosity to be well
constrained for 9 quasars. The derived average K-band absolute K-corrected host
galaxy magnitude for these luminous radio-quiet quasars is =-25.15+/-0.04,
slightly more luminous than an L* galaxy. The spread of derived host galaxy
luminosities is small, although the spread of nuclear-to-host ratios is not.
These host luminosities are shown to be comparable to those derived from
samples of quasars of lower total luminosity and we conclude that there is no
correlation between host and nuclear luminosity for these quasars.
Nuclear-to-host ratios break the lower limit previously suggested from studies
of lower nuclear luminosity quasars and Seyfert galaxies. Morphologies are less
certain but, on the scales probed by these images, some hosts appear to be
dominated by spheroids but others appear to have disk-dominated profiles.Comment: 16 pages, 8 figures, revised version to be published in MNRA
Constraining the Mass Profiles of Stellar Systems: Schwarzschild Modeling of Discrete Velocity Datasets
(ABRIDGED) We present a new Schwarzschild orbit-superposition code designed
to model discrete datasets composed of velocities of individual kinematic
tracers in a dynamical system. This constitutes an extension of previous
implementations that can only address continuous data in the form of (the
moments of) velocity distributions, thus avoiding potentially important losses
of information due to data binning. Furthermore, the code can handle any
combination of available velocity components, i.e., only line-of-sight
velocities, only proper motions, or a combination of both. It can also handle a
combination of discrete and continuous data. The code finds the distribution
function (DF, a function of the three integrals of motion E, Lz, and I3) that
best reproduces the available kinematic and photometric observations in a given
axisymmetric gravitational potential. The fully numerical approach ensures
considerable freedom on the form of the DF f(E,Lz,I3). This allows a very
general modeling of the orbital structure, thus avoiding restrictive
assumptions about the degree of (an)isotropy of the orbits. We describe the
implementation of the discrete code and present a series of tests of its
performance based on the modeling of simulated datasets generated from a known
DF. We find that the discrete Schwarzschild code recovers the original orbital
structure, M/L ratios, and inclination of the input datasets to satisfactory
accuracy, as quantified by various statistics. The code will be valuable, e.g.,
for modeling stellar motions in Galactic globular clusters, and those of
individual stars, planetary nebulae, or globular clusters in nearby galaxies.
This can shed new light on the total mass distributions of these systems, with
central black holes and dark matter halos being of particular interest.Comment: ApJ, in press; 51 pages, 11 figures; manuscript revised following
comments by refere
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