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Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…
A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We…
The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…
In a standard regression problem, we have a set of explanatory variables whose effect on some response vector is modeled. For wide binary data, such as genetic marker data, we often have two limitations. First, we have more parameters than…
The structure of large-scale social networks has predominantly been articulated using generative models, a form of average-case analysis. This chapter surveys recent proposals of more robust models of such networks. These models posit…
We extend the varying coefficient functional linear model to the nonlinear model and propose a varying coefficient functional additive model. The proposed method can represent the relationship between functional predictors and a scalar…
Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
In the era of "big data", it is becoming more of a challenge to not only build state-of-the-art predictive models, but also gain an understanding of what's really going on in the data. For example, it is often of interest to know which, if…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
Many forecasting applications have a limited distributed target variable, which is zero for most observations and positive for the remaining observations. In the econometrics literature, there is much research about statistical model…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…
We consider learning from labeled data collected across multiple environments, where the data distribution may vary across these environments. This problem is commonly approached from a causal perspective, seeking invariant representations…
Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive…