Search results for "Normality"
showing 10 items of 123 documents
Skewness in individual stocks at different investment horizons
2002
Abstract This paper examines the (a)symmetry of several individual stock returns at different investment horizons: daily, weekly and monthly. While some asymmetries are observed in daily returns, they disappear almost completely in weekly and monthly returns. The explanation for this fact lies in the convergence to normality that takes place when the investment horizon increases. These features allow one to question several financial models; in particular, they question the preference for positive skewness as a factor for investments in stock markets.
Extending graphical models for applications: on covariates, missingness and normality
2021
The authors of the paper “Bayesian Graphical Models for Modern Biological Applications” have put forward an important framework for making graphical models more useful in applied settings. In this discussion paper, we give a number of suggestions for making this framework even more suitable for practical scenarios. Firstly, we show that an alternative and simplified definition of covariate might make the framework more manageable in high-dimensional settings. Secondly, we point out that the inclusion of missing variables is important for practical data analysis. Finally, we comment on the effect that the Gaussianity assumption has in identifying the underlying conditional independence graph…
Testing abnormality in the spatial arrangement of cells in the corneal endothelium using spatial point processes
2001
The study of central corneal endothelium morphology is important in Ophthalmology. Some of the pathologies that could compromise endothelial cell morphology are trauma, cataract, surgery, use of contact lenses, corneal dystrophies or degenerations. The quantitative analysis of cell shape and cellular pattern is more sensitive in detecting subtle changes in endothelial morphology than cell density measurement or cell area analysis. In this paper, the morphology of the central cornea, the most important area from the point of view of vision, is studied through an associated bivariate spatial point pattern: the centroids of the cells and the triple points, that is, the points where three diffe…
Modeling Posidonia oceanica growth data: from linear to generalized linear mixed models
2010
The statistical analysis of annual growth of Posidonia oceanica is traditionally carried out through Gaussian linear models applied to untransformed, or log-transformed, data. In this paper, we claim that there are good reasons for re-considering this established practice, since real data on annual growth often violate the assumptions of Gaussian linear models, and show that the class of Generalized Linear Models (GLMs) represents a useful alternative for handling such violations. By analyzing Sicily PosiData-1, a real dataset on P. oceanica growth data gathered in the period 2000–2002 along the coasts of Sicily, we find that in the majority of cases Normality is rejected and the effect of …
Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous Diffusion
2017
We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality (LAN) jointly in $\theta$ and $T$ for the statistical experiment arising from continuous observation of this diffusion. The local scale turns out to be $n^{-1/2}$ for the shape parameter and $n^{-3/2}$ for the periodicity which generalizes known results about LAN when either $\theta$ or $T$ is assumed to be known.
Recursive estimation of the conditional geometric median in Hilbert spaces
2012
International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirm…
A more efficient second order blind identification method for separation of uncorrelated stationary time series
2016
The classical second order source separation methods use approximate joint diagonalization of autocovariance matrices with several lags to estimate the unmixing matrix. Based on recent asymptotic results, we propose a novel unmixing matrix estimator which selects the best lag set from a finite set of candidate sets specified by the user. The theory is illustrated by a simulation study.
Affine-invariant rank tests for multivariate independence in independent component models
2016
We consider the problem of testing for multivariate independence in independent component (IC) models. Under a symmetry assumption, we develop parametric and nonparametric (signed-rank) tests. Unlike in independent component analysis (ICA), we allow for the singular cases involving more than one Gaussian independent component. The proposed rank tests are based on componentwise signed ranks, à la Puri and Sen. Unlike the Puri and Sen tests, however, our tests (i) are affine-invariant and (ii) are, for adequately chosen scores, locally and asymptotically optimal (in the Le Cam sense) at prespecified densities. Asymptotic local powers and asymptotic relative efficiencies with respect to Wilks’…
Tests of Linearity, Multivariate Normality and the Adequacy of Linear Scores
1994
After some discussion of the purposes of testing multivariate normality, the paper concentrates on two different approaches to testing linearity: on repeated regression tests of non-linearity and on exploiting properties of a dichotomized normal distribution. Regression tests of linearity are used to examine the adequacy of linear scoring systems for explanatory variables, initially recorded on an ordinal scale. Examples from recent psychological and medical research are given in which the methods have led to some insight into subject-matter.
A note on finite PST-groups
2007
[EN] A finite group G is said to be a PST-group if, for subgroups H and K of G with H Sylow-permutable in K and K Sylow-permutable in G, it is always the case that H is Sylow-permutable in G. A group G is a T*-group if, for subgroups H and K of G with H normal in K and K normal in G, it is always the case that H is Sylow-permutable in G. In this paper, we show that finite PST-groups and finite T*-groups are one and the same. A new characterisation of soluble PST-groups is also presented.