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This short book elaborates on selected aspects of stochastic-statistical dependencies in multivariate statistics. Each chapter provides a rigorous and self-contained treatment of one specific topic, poses a particular problem within its scope, and concludes by presenting its solution. The presented problems are not only relevant for research in mathematical statistics, but also entertaining, with elegant proofs and appealing solutions. The chapters cover correlation coefficients of bivariate normal distributions, empirical likelihood ratio tests for the population correlation, the rearrangement algorithm, covariances of order statistics, equi-correlation matrices, skew-normal distributions and the weighted bootstrap. This book is primarily intended for early-career researchers in mathematical statistics, but will also be interesting for lecturers in the field. Its goal is to rouse the reader's interest, further their knowledge of the subject and provide them with some useful mathematical techniques.

Statistical science --- Mathematical statistics --- statistiek --- statistisch onderzoek --- Multivariate analysis. --- Dependence (Statistics) --- Anàlisi multivariable

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Matrius (Matemàtica) --- Desigualtats (Matemàtica) --- Processos infinits --- Desigualtats isoperimètriques --- Àlgebra de matrius --- Àlgebra matricial --- Càlcul de matrius --- Càlcul matricial --- Matrius (Àlgebra) --- Àlgebra abstracta --- Àlgebra universal --- Anàlisi multivariable --- Diagrames de Feynman --- Grups modulars --- Jocs d'estratègia (Matemàtica) --- Matrius aleatòries --- Matrius disperses --- Programació lineal --- Desigualtats matricials --- Desigualtats de matrius --- Matrix inequalities. --- Operator theory. --- Functional analysis --- Inequalities (Mathematics) --- Matrices

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Matrius aleatòries --- Anàlisi multivariable --- Anàlisi multivariant --- Estadística matemàtica --- Matrius (Matemàtica) --- Anàlisi de conglomerats --- Anàlisi de correspondències (Estadística) --- Anàlisi discriminant --- Modelització multiescala --- Models d'equacions estructurals --- Anàlisi conjunt (Màrqueting) --- Random matrices. --- Asymptotic efficiencies (Statistics) --- Multivariate analysis. --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Mathematical statistics --- Matrices --- Efficiencies, Asymptotic (Statistics) --- Estimation theory --- Statistical hypothesis testing --- Matrices, Random

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Multivariate statistical analysis has undergone a rich and varied evolution during the latter half of the 20th century. Academics and practitioners have produced much literature with diverse interests and with varying multidisciplinary knowledge on different topics within the multivariate domain. Due to multivariate algebra being of sustained interest and being a continuously developing field, its appeal breaches laterally across multiple disciplines to act as a catalyst for contemporary advances, with its core inferential genesis remaining in that of statistics. It is exactly this varied evolution caused by an influx in data production, diffusion, and understanding in scientific fields that has blurred many lines between disciplines. The cross-pollination between statistics and biology, engineering, medical science, computer science, and even art, has accelerated the vast amount of questions that statistical methodology has to answer and report on. These questions are often multivariate in nature, hoping to elucidate uncertainty on more than one aspect at the same time, and it is here where statistical thinking merges mathematical design with real life interpretation for understanding this uncertainty. Statistical advances benefit from these algebraic inventions and expansions in the multivariate paradigm. This contributed volume aims to usher novel research emanating from a multivariate statistical foundation into the spotlight, with particular significance in multidisciplinary settings. The overarching spirit of this volume is to highlight current trends, stimulate a focus on, and connect multidisciplinary dots from and within multivariate statistical analysis. Guided by these thoughts, a collection of research at the forefront of multivariate statistical thinking is presented here which has been authored by globally recognized subject matter experts.

Mathematics. --- Anàlisi multivariable --- Math --- Science --- Anàlisi multivariant --- Estadística matemàtica --- Matrius (Matemàtica) --- Anàlisi de conglomerats --- Anàlisi de correspondències (Estadística) --- Anàlisi discriminant --- Modelització multiescala --- Models d'equacions estructurals --- Anàlisi conjunt (Màrqueting) --- Statistics. --- Applied Statistics. --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics

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Mathematical statistics. --- Mathematical statistics --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Estadística matemàtica --- Estadística descriptiva --- Inferència estadística --- Matemàtica estadística --- Mètodes estadístics --- Estadística --- Anàlisi d'error (Matemàtica) --- Anàlisi de regressió --- Anàlisi de sèries temporals --- Anàlisi de variància --- Anàlisi multivariable --- Anàlisi seqüencial --- Astronomia estadística --- Correlació (Estadística) --- Dependència (Estadística) --- Estadística no paramètrica --- Estadística robusta --- Física estadística --- Mètode dels moments (Estadística) --- Models lineals (Estadística) --- Models no lineals (Estadística) --- Teoria de l'estimació --- Teoria de la predicció --- Tests d'hipòtesi (Estadística) --- Biometria --- Mostreig (Estadística)