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Big Data often presents as massive non-probability samples. Not only is the selection mechanism often unknown, but larger data volume amplifies the relative contribution of selection bias to total error. Existing bias adjustment approaches…

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…

In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting…

Robust regression has attracted a great amount of attention in the literature recently, particularly for taking asymmetricity into account simultaneously and for high-dimensional analysis. However, the majority of research on the topics…

Imputation of data with general structures (e.g., data with continuous, binary, unordered categorical, and ordinal variables) is commonly performed with fully conditional specification (FCS) instead of joint modeling. A key drawback of FCS…

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…

To model categorical response variables given their covariates, we propose a permuted and augmented stick-breaking (paSB) construction that one-to-one maps the observed categories to randomly permuted latent sticks. This new construction…

This paper develops a framework for quantile regression in binary longitudinal data settings. A novel Markov chain Monte Carlo (MCMC) method is designed to fit the model and its computational efficiency is demonstrated in a simulation…

We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber--White sandwich estimator. The sandwich estimator is known to provide asymptotically…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

Modeling and predicting extreme movements in GDP is notoriously difficult and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our focus is on using large…

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…

Bayes spaces were initially designed to provide a geometric framework for the modeling and analysis of distributional data. It has recently come to light that this methodology can be exploited to provide an orthogonal decomposition of…

Catastrophic loss data are known to be heavy-tailed. Practitioners then need models that are able to capture both tail and modal parts of claim data. To this purpose, a new parametric family of loss distributions is proposed as a gamma…

In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as beta-exponential and generalized Gompertz…

Irregular errors such as heteroscedasticity and nonnormality remain major challenges in linear modeling. These issues often lead to biased inference and unreliable measures of uncertainty. Classical remedies, such as robust standard errors…

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…

Lasso is a popular and efficient approach to simultaneous estimation and variable selection in high-dimensional regression models. In this paper, a robust LAD-lasso method for multiple outcomes is presented that addresses the challenges of…

There is a growing interest in learning how the distribution of a response variable changes with a set of predictors. Bayesian nonparametric dependent mixture models provide a flexible approach to address this goal. However, several…

We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…