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We present a multidimensional data analysis framework for the analysis of ordinal response variables. Underlying the ordinal variables, we assume a continuous latent variable, leading to cumulative logit models. The framework includes…

Multivariate correlation analysis plays a key role in various fields such as statistics and big data analytics. In this paper, it is presented a new non-parametric association measure between more than two variables based on the concept of…

A simple generative model for rank ordered data with ties is presented. The model is based on ordering geometric latent variables and can be seen as the discrete counterpart of the Plackett-Luce (PL) model, a popular, relatively tractable…

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected…

Dependence modeling of multivariate count data has garnered significant attention in recent years. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of…

We introduce a copula mixture model to perform dependency-seeking clustering when co-occurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend…

Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the…

Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…

We present an approach for modeling and imputation of nonignorable missing data. Our approach uses Bayesian data integration to combine (1) a Gaussian copula model for all study variables and missingness indicators, which allows arbitrary…

Copula models have been widely used to model the dependence between continuous random variables, but modeling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective…

We exploit Gaussian copulas to specify a class of multivariate circular distributions and obtain parametric models for the analysis of correlated circular data. This approach provides a straightforward extension of traditional multivariate…

Missing value imputation is crucial for real-world data science workflows. Imputation is harder in the online setting, as it requires the imputation method itself to be able to evolve over time. For practical applications, imputation…

Item nonresponse is frequently encountered in practice. Ignoring missing data can lose efficiency and lead to misleading inference. Fractional imputation is a frequentist approach of imputation for handling missing data. However, the…

Modern large scale datasets are often plagued with missing entries. For tabular data with missing values, a flurry of imputation algorithms solve for a complete matrix which minimizes some penalized reconstruction error. However, almost…

Modern datasets commonly feature both substantial missingness and many variables of mixed data types, which present significant challenges for estimation and inference. Complete case analysis, which proceeds using only the observations with…

Motivated by challenges in the analysis of biomedical data and observational studies, we develop statistical boosting for the general class of bivariate distributional copula regression with arbitrary marginal distributions, which is suited…

We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding…

Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…

This paper studies the binary classification of two distributions with the same Gaussian copula in high dimensions. Under this semiparametric Gaussian copula setting, we derive an accurate semiparametric estimator of the log density ratio,…

We develop a robust data fusion algorithm for field reconstruction of multiple physical phenomena. The contribution of this paper is twofold: First, we demonstrate how multi-spatial fields which can have any marginal distributions and…