10,238 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
Exact asymptotic distribution of change-point mle for change in the mean of Gaussian sequences
We derive exact computable expressions for the asymptotic distribution of the
change-point mle when a change in the mean occurred at an unknown point of a
sequence of time-ordered independent Gaussian random variables. The derivation,
which assumes that nuisance parameters such as the amount of change and
variance are known, is based on ladder heights of Gaussian random walks hitting
the half-line. We then show that the exact distribution easily extends to the
distribution of the change-point mle when a change occurs in the mean vector of
a multivariate Gaussian process. We perform simulations to examine the accuracy
of the derived distribution when nuisance parameters have to be estimated as
well as robustness of the derived distribution to deviations from Gaussianity.
Through simulations, we also compare it with the well-known conditional
distribution of the mle, which may be interpreted as a Bayesian solution to the
change-point problem. Finally, we apply the derived methodology to monthly
averages of water discharges of the Nacetinsky creek, Germany.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS294 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Classical and Bayesian Inference of a Mixture of Bivariate Exponentiated Exponential Model
Exponentiated exponential (EE) model has been used effectively in reliability, engineering, biomedical, social sciences, and other applications. In this study, we introduce a new bivariate mixture EE model with two parameters assuming two cases, independent and dependent random variables. We develop a bivariate mixture starting from two EE models assuming two cases, two independent and two dependent EE models. We study some useful statistical properties of this distribution, such as marginals and conditional distributions and product moments and conditional moments. In addition, we study a dependent case, a new mixture of the bivariate model based on EE distribution marginal with two parameters and with a bivariate Gaussian copula. Different methods of estimation for the model parameters are used both under the classical and under the Bayesian paradigm. Some simulation studies are presented to verify the performance of the estimation methods of the proposed model. To illustrate the flexibility of the proposed model, a real dataset is reanalyzed
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