Related papers: An Introduction to Copulas: a Complement
We propose a copula based method to handle missing values in multivariate data of mixed types in multilevel data sets. Building upon the extended rank likelihood of \cite{hoff2007extending} and the multinomial probit model, our model is a…
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
This is the first in a set of three papers providing an introduction to generalised Cesaro convergence. We start with traditional Cesaro methods for extending classical convergence and further generalise these to allow the calculation of…
Probability density estimation is a central task in statistics. Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions…
A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce.…
The main goal of this paper is to study the extent of freedom one has in constructing quasi-copulas vs. copulas. Specifically, it exhibits three construction methods for quasi-copulas based on recent developments: a representation of…
We propose a copula density estimator that can include information on bivariate marginals when the information is available. We use B-splines for copula density approximation and include information on bivariate marginals via a penalty…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
We prove that every quasi-copula can be written as a uniformly converging infinite sum of multiples of copulas. Furthermore, we characterize those quasi-copulas which can be written as a finite sum of multiples of copulas, i.e., that are a…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
Two key ingredients to carry out inference on the copula of multivariate observations are the empirical copula process and an appropriate resampling scheme for the latter. Among the existing techniques used for i.i.d. observations, the…
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…
W-transforms are introduced as uniformity-preserving univariate transformations on the unit interval induced by distribution functions and piecewise strictly monotone functions, and their properties are investigated. When applied…
A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The…
In causal inference with ordinal outcomes, several interpretable estimands are functions of the probability that the potential outcome under one treatment is larger than that under another treatment for the same unit. This probability…
Given a random sample from a continuous multivariate distribution, Stute's representation is obtained for empirical copula processes constructed from a broad class of smooth, possibly data-adaptive nonparametric copula estimators. The…