53,764 research outputs found
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
No-reference image quality assessment through the von Mises distribution
An innovative way of calculating the von Mises distribution (VMD) of image
entropy is introduced in this paper. The VMD's concentration parameter and some
fitness parameter that will be later defined, have been analyzed in the
experimental part for determining their suitability as a image quality
assessment measure in some particular distortions such as Gaussian blur or
additive Gaussian noise. To achieve such measure, the local R\'{e}nyi entropy
is calculated in four equally spaced orientations and used to determine the
parameters of the von Mises distribution of the image entropy. Considering
contextual images, experimental results after applying this model show that the
best-in-focus noise-free images are associated with the highest values for the
von Mises distribution concentration parameter and the highest approximation of
image data to the von Mises distribution model. Our defined von Misses fitness
parameter experimentally appears also as a suitable no-reference image quality
assessment indicator for no-contextual images.Comment: 29 pages, 11 figure
Empirical Bayesian Approach to Testing Multiple Hypotheses with Separate Priors for Left and Right Alternatives
We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of data from biological experiments: HIV-transfected cell-line mRNA expression data, and a quantitative trait genome-wide SNP data set. We have developed a user-friendly web-based shiny App for the proposed method which is available through URL https://npseb.shinyapps.io/npseb/. The HIV and SNP data can be directly accessed, and the results presented in this paper can be executed
Statistical identification with hidden Markov models of large order splitting strategies in an equity market
Large trades in a financial market are usually split into smaller parts and
traded incrementally over extended periods of time. We address these large
trades as hidden orders. In order to identify and characterize hidden orders we
fit hidden Markov models to the time series of the sign of the tick by tick
inventory variation of market members of the Spanish Stock Exchange. Our
methodology probabilistically detects trading sequences, which are
characterized by a net majority of buy or sell transactions. We interpret these
patches of sequential buying or selling transactions as proxies of the traded
hidden orders. We find that the time, volume and number of transactions size
distributions of these patches are fat tailed. Long patches are characterized
by a high fraction of market orders and a low participation rate, while short
patches have a large fraction of limit orders and a high participation rate. We
observe the existence of a buy-sell asymmetry in the number, average length,
average fraction of market orders and average participation rate of the
detected patches. The detected asymmetry is clearly depending on the local
market trend. We also compare the hidden Markov models patches with those
obtained with the segmentation method used in Vaglica {\it et al.} (2008) and
we conclude that the former ones can be interpreted as a partition of the
latter ones.Comment: 26 pages, 12 figure
Empirical Bayesian Approach to Testing Multiple Hypotheses with Separate Priors for Left and Right Alternatives
We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of data from biological experiments: HIV-transfected cell-line mRNA expression data, and a quantitative trait genome-wide SNP data set. We have developed a user-friendly web-based shiny App for the proposed method which is available through URL https://npseb.shinyapps.io/npseb/. The HIV and SNP data can be directly accessed, and the results presented in this paper can be executed
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