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Using Multivariate Statistics

Matrix Differential Calculus with Applications in Statistics and Econometrics

Tables of integrals

Probability and Measure

This article updates the guidance published in 2015 for authors submitting papers to British Journal of Pharmacology (Curtis et al., 2015) and is intended to provide the rubric for peer review. Thus, it is directed towards authors, reviewers and editors. Explanations for many of the requirements were outlined previously and are not restated here. The new guidelines are intended to replace those published previously. The guidelines have been simplified for ease of understanding by authors, to make it more straightforward for peer reviewers to check compliance and to facilitate the curation of the journal's efforts to improve standards.

/pdf/experimental-design-and-analysis-and-their-reporting-ii-56ml693gqr.pdf

Experimental design and analysis and their reporting II: updated and simplified guidance for authors and peer reviewers

Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median

Detecting multivariate outliers: Use a robust variant of the Mahalanobis distance

Modern Directional Statistics collects important advances in methodology and theory for directional statistics over the last two decades. It provides a detailed overview and analysis of recent results that can help both researchers and practitioners. Knowledge of multivariate statistics eases the reading but is not mandatory.

The field of directional statistics has received a lot of attention over the past two decades, due to new demands from domains such as life sciences or machine learning, to the availability of massive data sets requiring adapted statistical techniques, and to technological advances. This book covers important progresses in distribution theory,high-dimensional statistics, kernel density estimation, efficient inference on directional supports, and computational and graphical methods. 
Christophe Ley is professor of mathematical statistics at Ghent University. His research interests include semi-parametrically efficient inference, flexible modeling, directional statistics and the study of asymptotic approximations via Stein’s Method. His achievements include the Marie-Jeanne Laurent-Duhamel prize of the Societe Francaise de Statistique and an elected membership at the International Statistical Institute. He is associate editor for the journals Computational Statistics & Data Analysis and Econometrics and Statistics.

Thomas Verdebout is professor of mathematical statistics at Universite libre de Bruxelles (ULB). His main research interests are semi-parametric statistics, high- dimensional statistics, directional statistics and rank-based procedures. He has won an annual prize of the Belgian Academy of Sciences and is an elected member of the International Statistical Institute. He is associate editor for the journals Statistics and Probability Letters and Journal of Multivariate Analysis.

Modern Directional Statistics

Researchers often lack knowledge about how to deal with outliers when analyzing their data. Even more frequently, researchers do not pre-specify how they plan to manage outliers. In this paper we aim to improve research practices by outlining what you need to know about outliers. We start by providing a functional definition of outliers. We then lay down an appropriate nomenclature/classification of outliers. This nomenclature is used to understand what kinds of outliers can be encountered and serves as a guideline to make appropriate decisions regarding the conservation, deletion, or recoding of outliers. These decisions might impact the validity of statistical inferences as well as the reproducibility of our experiments. To be able to make informed decisions about outliers you first need proper detection tools. We remind readers why the most common outlier detection methods are problematic and recommend the use of the median absolute deviation to detect univariate outliers, and of the Mahalanobis-MCD distance to detect multivariate outliers. An R package was created that can be used to easily perform these detection tests. Finally, we promote the use of pre-registration to avoid flexibility in data analysis when handling outliers.

https://biblio.ugent.be/publication/8619726/file/8646347.pdf

How to classify, detect, and manage univariate and multivariate outliers, with emphasis on pre-registration

We propose a new general version of Stein’s method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution which is based on a linear difference or differential-type operator. The resulting Stein identity highlights the unifying theme behind the literature on Stein’s method (both for continuous and discrete distributions). Viewing the Stein operator as an operator acting on pairs of functions, we provide an extensive toolkit for distributional comparisons. Several abstract approximation theorems are provided. Our approach is illustrated for comparison of several pairs of distributions: normal vs normal, sums of independent Rademacher vs normal, normal vs Student, and maximum of random variables vs exponential, Frechet and Gumbel.

https://projecteuclid.org/download/pdfview_1/euclid.ps/1483952471

Christophe Ley

Papers

Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median

Detecting multivariate outliers: Use a robust variant of the Mahalanobis distance

Modern Directional Statistics

How to classify, detect, and manage univariate and multivariate outliers, with emphasis on pre-registration

Stein's method for comparison of univariate distributions