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Register a new userMaxSkew and MultiSkew: Two R Packages for Detecting, Measuring and Removing Multivariate Skewness
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Added by
Cinzia Franceschini
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
Authors
Cinzia Franceschini
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No Arabic abstract
Skewness plays a relevant role in several multivariate statistical techniques. Sometimes it is used to recover data features, as in cluster analysis. In other circumstances, skewness impairs the performances of statistical methods, as in the Hotellings one-sample test. In both cases, there is the need to check the symmetry of the underlying distribution, either by visual inspection or by formal testing. The R packages MaxSkew and MultiSkew address these issues by measuring, testing and removing skewness from multivariate data. Skewness is assessed by the third multivariate cumulant and its functions. The hypothesis of symmetry is tested either nonparametrically, with the bootstrap, or parametrically, under the normality assumption. Skewness is removed or at least alleviated by projecting the data onto appropriate linear subspaces. Usages of MaxSkew and MultiSkew are illustrated with the Iris dataset.
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The R-package REPPlab is designed to explore multivariate data sets using one-dimensional unsupervised projection pursuit. It is useful in practice as a preprocessing step to find clusters or as an outlier detection tool for multivariate numerical data. Except from the package tourr that implements smooth sequences of projection matrices and rggobi that provides an interface to a dynamic graphics package called GGobi, there is no implementation of exploratory projection pursuit tools available in R especially in the context of outlier detection. REPPlab is an R interface for the Java program EPPlab that implements four projection indices and three biologically inspired optimization algorithms. The implemented indices are either adapted to cluster or to outlier detection and the optimization algorithms have at most one parameter to tune. Following the original software EPPlab, the exploration strategy in REPPlab is divided into two steps. Many potentially interesting projections are calculated at the first step and examined at the second step. For this second step, different tools for plotting and combining the results are proposed with specific tools for outlier detection. Compared to EPPlab, some of these tools are new and their performance is illustrated through some simulations and using some real data sets in a clustering context. The functionalities of the package are also illustrated for outlier detection on a new data set that is provided with the package.
The R package MfUSampler provides Monte Carlo Markov Chain machinery for generating samples from multivariate probability distributions using univariate sampling algorithms such as Slice Sampler and Adaptive Rejection Sampler. The sampler function performs a full cycle of univariate sampling steps, one coordinate at a time. In each step, the latest sample values obtained for other coordinates are used to form the conditional distributions. The concept is an extension of Gibbs sampling where each step involves, not an independent sample from the conditional distribution, but a Markov transition for which the conditional distribution is invariant. The software relies on proportionality of conditional distributions to the joint distribution to implement a thin wrapper for producing conditionals. Examples illustrate basic usage as well as methods for improving performance. By encapsulating the multivariate-from-univariate logic, MfUSampler provides a reliable library for rapid prototyping of custom Bayesian models while allowing for incremental performance optimizations such as utilization of conjugacy, conditional independence, and porting function evaluations to compiled languages.
In this paper, a new mixture family of multivariate normal distributions, formed by mixing multivariate normal distribution and skewed distribution, is constructed. Some properties of this family, such as characteristic function, moment generating function, and the first four moments are derived. The distributions of affine transformations and canonical forms of the model are also derived. An EM type algorithm is developed for the maximum likelihood estimation of model parameters. We have considered in detail, some special cases of the family, using standard gamma and standard exponential mixture distributions, denoted by MMNG and MMNE, respectively. For the proposed family of distributions, different multivariate measures of skewness are computed. In order to examine the performance of the developed estimation method, some simulation studies are carried out to show that the maximum likelihood estimates based on the EM type algorithm do provide good performance. For different choices of parameters of MMNE distribution, several multivariate measures of skewness are computed and compared. Because some measures of skewness are scalar and some are vectors, in order to evaluate them properly, we have carried out a simulation study to determine the power of tests, based on samp
Modelling multivariate systems is important for many applications in engineering and operational research. The multivariate distributions under scrutiny usually have no analytic or closed form. Therefore their modelling employs a numerical technique, typically multivariate simulations, which can have very high dimensions. Random Orthogonal Matrix (ROM) simulation is a method that has gained some popularity because of the absence of certain simulation errors. Specifically, it exactly matches a target mean, covariance matrix and certain higher moments with every simulation. This paper extends the ROM simulation algorithm presented by Hanke et al. (2017), hereafter referred to as HPSW, which matches the target mean, covariance matrix and Kollo skewness vector exactly. Our first contribution is to establish necessary and sufficient conditions for the HPSW algorithm to work. Our second contribution is to develop a general approach for constructing admissible values in the HPSW. Our third theoretical contribution is to analyse the effect of multivariate sample concatenation on the target Kollo skewness. Finally, we illustrate the extensions we develop here using a simulation study.
FRK is an R software package for spatial/spatio-temporal modelling and prediction with large datasets. It facilitates optimal spatial prediction (kriging) on the most commonly used manifolds (in Euclidean space and on the surface of the sphere), for both spatial and spatio-temporal fields. It differs from many of the packages for spatial modelling and prediction by avoiding stationary and isotropic covariance and variogram models, instead constructing a spatial random effects (SRE) model on a fine-resolution discretised spatial domain. The discrete element is known as a basic areal unit (BAU), whose introduction in the software leads to several practical advantages. The software can be used to (i) integrate multiple observations with different supports with relative ease; (ii) obtain exact predictions at millions of prediction locations (without conditional simulation); and (iii) distinguish between measurement error and fine-scale variation at the resolution of the BAU, thereby allowing for reliable uncertainty quantification. The temporal component is included by adding another dimension. A key component of the SRE model is the specification of spatial or spatio-temporal basis functions; in the package, they can be generated automatically or by the user. The package also offers automatic BAU construction, an expectation-maximisation (EM) algorithm for parameter estimation, and functionality for prediction over any user-specified polygons or BAUs. Use of the package is illustrated on several spatial and spatio-temporal datasets, and its predictions and the model it implements are extensively compared to others commonly used for spatial prediction and modelling.
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