Related papers: Implicit Copulas: An Overview
The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions…
We develop factor copula models for analysing the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric…
Copula is a powerful tool to model multivariate data. We propose the modelling of intraday financial returns of multiple assets through copula. The problem originates due to the asynchronous nature of intraday financial data. We propose a…
Non-random sample selection is a commonplace amongst many empirical studies and it appears when an output variable of interest is available only for a restricted non-random sub-sample of data. We introduce an extension of the generalized…
We introduce a class of copulas that we call Principal Component Copulas (PCCs). This class combines the strong points of copula-based techniques with principal component analysis (PCA), which results in flexibility when modelling tail…
Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenarios, models exhibiting heavy tails in the margins and…
We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression…
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer…
Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the…
We propose to construct copulas from the inversion of nonlinear state space models. These allow for new time series models that have the same serial dependence structure of a state space model, but with an arbitrary marginal distribution,…
We propose a new copula model that can be used with replicated spatial data. Unlike the multivariate normal copula, the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all…
Copula modelling has in the past decade become a standard tool in many areas of applied statistics. However, a largely neglected aspect concerns the design of related experiments. Particularly the issue of whether the estimation of copula…
Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a…
We propose a copula-based extension of the hidden Markov model (HMM) which applies when the observations recorded at each time in the sample are multivariate. The joint model produced by the copula extension allows decoding of the hidden…
Model selection is an important activity in modern data analysis and the conventional Bayesian approach to this problem involves calculation of marginal likelihoods for different models, together with diagnostics which examine specific…
Prior elicitation methods for Bayesian analyses transfigure prior information into quantifiable prior distributions. Recently, methods that leverage copulas have been proposed to accommodate more flexible dependence structures when…
Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…
Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to…