cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.7015253.v3
title: A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies

description: Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high dimensional, has been proposed to analyze multiple correlated phenotypes. It has been empirically observed that the first PC, which summarizes the largest amount of variance, can be less powerful than higher-order PCs and other commonly used methods in detecting genetic association signals. In this article, we investigate the properties of PCA-based multiple phenotype analysis from a geometric perspective by introducing a novel concept called principal angle. A particular PC is powerful if its principal angle is 0° and is powerless if its principal angle is 90°. Without prior knowledge about the true principal angle, each PC can be powerless. We propose linear, nonlinear, and data-adaptive omnibus tests by combining PCs. We demonstrate that the Wald test is a special quadratic PC-based test. We show that the omnibus PC test is robust and powerful in a wide range of scenarios. We study the properties of the proposed methods using power analysis and eigen-analysis. The subtle differences and close connections between these combined PC methods are illustrated graphically in terms of their rejection boundaries. Our proposed tests have convex acceptance regions and hence are admissible. The <i>p</i>-values for the proposed tests can be efficiently calculated analytically and the proposed tests have been implemented in a publicly available R package <i>MPAT</i>. We conduct simulation studies in both low- and high-dimensional settings with various signal vectors and correlation structures. We apply the proposed tests to the joint analysis of metabolic syndrome-related phenotypes with datasets collected from four international consortia to demonstrate the effectiveness of the proposed combined PC testing procedures. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.6213902
title: An Adapted Loss Function for Censored Quantile Regression

description: In this article, we study a novel approach for the estimation of quantiles when facing potential right censoring of the responses. Contrary to the existing literature on the subject, the adopted strategy of this article is to tackle censoring at the very level of the loss function usually employed for the computation of quantiles, the so-called “check” function. For interpretation purposes, a simple comparison with the latter reveals how censoring is accounted for in the newly proposed loss function. Subsequently, when considering the inclusion of covariates for conditional quantile estimation, by defining a new general loss function the proposed methodology opens the gate to numerous parametric, semiparametric, and nonparametric modeling techniques. To illustrate this statement, we consider the well-studied linear regression under the usual assumption of conditional independence between the true response and the censoring variable. For practical minimization of the studied loss function, we also provide a simple algorithmic procedure shown to yield satisfactory results for the proposed estimator with respect to the existing literature in an extensive simulation study. From a more theoretical prospect, consistency and asymptotic normality of the estimator for linear regression are obtained using several recent results on nonsmooth semiparametric estimation equations with an infinite-dimensional nuisance parameter, while numerical examples illustrate the adequateness of a simple bootstrap procedure for inferential purposes. Lastly, an application to a real dataset is used to further illustrate the validity and finite sample performance of the proposed estimator. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7445663.v2
title: Spatial Homogeneity Pursuit of Regression Coefficients for Large Datasets

description: Spatial regression models have been widely used to describe the relationship between a response variable and some explanatory variables over a region of interest, taking into account the spatial dependence of the observations. In many applications, relationships between response variables and covariates are expected to exhibit complex spatial patterns. We propose a new approach, referred to as spatially clustered coefficient (SCC) regression, to detect spatially clustered patterns in the regression coefficients. It incorporates spatial neighborhood information through a carefully constructed regularization to automatically detect change points in space and to achieve computational scalability. Our numerical studies suggest that SCC works very effectively, capturing not only clustered coefficients, but also smoothly varying coefficients because of its strong local adaptivity. This flexibility allows researchers to explore various spatial structures in regression coefficients. We also establish theoretical properties of SCC. We use SCC to explore the relationship between the temperature and salinity of sea water in the Atlantic basin; this can provide important insights about the evolution of individual water masses and the pathway and strength of meridional overturning circulation in oceanography. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.6406049
title: Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition

description: We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume that the domain has a boundary with positive reach. We propose a data-splitting approach to correct the bias of the plug-in estimator based on the sample α-convex hull. We show that this simple estimator achieves a minimax lower bound that we derive. Some numerical experiments corroborate our theoretical findings. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.6406049.v3
title: Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition

description: We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume that the domain has a boundary with positive reach. We propose a data-splitting approach to correct the bias of the plug-in estimator based on the sample α-convex hull. We show that this simple estimator achieves a minimax lower bound that we derive. Some numerical experiments corroborate our theoretical findings. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7578017
title: Limits to Human Life Span Through Extreme Value Theory

description: There is no scientific consensus on the fundamental question whether the probability distribution of the human life span has a finite endpoint or not and, if so, whether this upper limit changes over time. Our study uses a unique dataset of the ages at death—in days—of all (about 285,000) Dutch residents, born in the Netherlands, who died in the years 1986–2015 at a minimum age of 92 years and is based on extreme value theory, the coherent approach to research problems of this type. Unlike some other studies, we base our analysis on the configuration of thousands of mortality data of old people, not just the few oldest old. We find compelling statistical evidence that there is indeed an upper limit to the life span of men and to that of women for all the 30 years we consider and, moreover, that there are no indications of trends in these upper limits over the last 30 years, despite the fact that the number of people reaching high age (say 95 years) was almost tripling. We also present estimates for the endpoints, for the force of mortality at very high age, and for the so-called perseverance parameter. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.6213902.v2
title: An Adapted Loss Function for Censored Quantile Regression

description: In this article, we study a novel approach for the estimation of quantiles when facing potential right censoring of the responses. Contrary to the existing literature on the subject, the adopted strategy of this article is to tackle censoring at the very level of the loss function usually employed for the computation of quantiles, the so-called “check” function. For interpretation purposes, a simple comparison with the latter reveals how censoring is accounted for in the newly proposed loss function. Subsequently, when considering the inclusion of covariates for conditional quantile estimation, by defining a new general loss function the proposed methodology opens the gate to numerous parametric, semiparametric, and nonparametric modeling techniques. To illustrate this statement, we consider the well-studied linear regression under the usual assumption of conditional independence between the true response and the censoring variable. For practical minimization of the studied loss function, we also provide a simple algorithmic procedure shown to yield satisfactory results for the proposed estimator with respect to the existing literature in an extensive simulation study. From a more theoretical prospect, consistency and asymptotic normality of the estimator for linear regression are obtained using several recent results on nonsmooth semiparametric estimation equations with an infinite-dimensional nuisance parameter, while numerical examples illustrate the adequateness of a simple bootstrap procedure for inferential purposes. Lastly, an application to a real dataset is used to further illustrate the validity and finite sample performance of the proposed estimator. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7578017.v3
title: Limits to Human Life Span Through Extreme Value Theory

description: There is no scientific consensus on the fundamental question whether the probability distribution of the human life span has a finite endpoint or not and, if so, whether this upper limit changes over time. Our study uses a unique dataset of the ages at death—in days—of all (about 285,000) Dutch residents, born in the Netherlands, who died in the years 1986–2015 at a minimum age of 92 years and is based on extreme value theory, the coherent approach to research problems of this type. Unlike some other studies, we base our analysis on the configuration of thousands of mortality data of old people, not just the few oldest old. We find compelling statistical evidence that there is indeed an upper limit to the life span of men and to that of women for all the 30 years we consider and, moreover, that there are no indications of trends in these upper limits over the last 30 years, despite the fact that the number of people reaching high age (say 95 years) was almost tripling. We also present estimates for the endpoints, for the force of mortality at very high age, and for the so-called perseverance parameter. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.6213902.v1
title: An Adapted Loss Function for Censored Quantile Regression

description: In this article, we study a novel approach for the estimation of quantiles when facing potential right censoring of the responses. Contrary to the existing literature on the subject, the adopted strategy of this article is to tackle censoring at the very level of the loss function usually employed for the computation of quantiles, the so-called “check” function. For interpretation purposes, a simple comparison with the latter reveals how censoring is accounted for in the newly proposed loss function. Subsequently, when considering the inclusion of covariates for conditional quantile estimation, by defining a new general loss function the proposed methodology opens the gate to numerous parametric, semiparametric, and nonparametric modeling techniques. To illustrate this statement, we consider the well-studied linear regression under the usual assumption of conditional independence between the true response and the censoring variable. For practical minimization of the studied loss function, we also provide a simple algorithmic procedure shown to yield satisfactory results for the proposed estimator with respect to the existing literature in an extensive simulation study. From a more theoretical prospect, consistency and asymptotic normality of the estimator for linear regression are obtained using several recent results on nonsmooth semiparametric estimation equations with an infinite-dimensional nuisance parameter, while numerical examples illustrate the adequateness of a simple bootstrap procedure for inferential purposes. Lastly, an application to a real dataset is used to further illustrate the validity and finite sample performance of the proposed estimator. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.6406049.v2
title: Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition

description: We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume that the domain has a boundary with positive reach. We propose a data-splitting approach to correct the bias of the plug-in estimator based on the sample α-convex hull. We show that this simple estimator achieves a minimax lower bound that we derive. Some numerical experiments corroborate our theoretical findings. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7445663.v1
title: Spatial Homogeneity Pursuit of Regression Coefficients for Large Datasets

description: Spatial regression models have been widely used to describe the relationship between a response variable and some explanatory variables over a region of interest, taking into account the spatial dependence of the observations. In many applications, relationships between response variables and covariates are expected to exhibit complex spatial patterns. We propose a new approach, referred to as spatially clustered coefficient (SCC) regression, to detect spatially clustered patterns in the regression coefficients. It incorporates spatial neighborhood information through a carefully constructed regularization to automatically detect change points in space and to achieve computational scalability. Our numerical studies suggest that SCC works very effectively, capturing not only clustered coefficients, but also smoothly varying coefficients because of its strong local adaptivity. This flexibility allows researchers to explore various spatial structures in regression coefficients. We also establish theoretical properties of SCC. We use SCC to explore the relationship between the temperature and salinity of sea water in the Atlantic basin; this can provide important insights about the evolution of individual water masses and the pathway and strength of meridional overturning circulation in oceanography. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.7578017.v2
title: Limits to Human Life Span Through Extreme Value Theory

description: There is no scientific consensus on the fundamental question whether the probability distribution of the human life span has a finite endpoint or not and, if so, whether this upper limit changes over time. Our study uses a unique dataset of the ages at death—in days—of all (about 285,000) Dutch residents, born in the Netherlands, who died in the years 1986–2015 at a minimum age of 92 years and is based on extreme value theory, the coherent approach to research problems of this type. Unlike some other studies, we base our analysis on the configuration of thousands of mortality data of old people, not just the few oldest old. We find compelling statistical evidence that there is indeed an upper limit to the life span of men and to that of women for all the 30 years we consider and, moreover, that there are no indications of trends in these upper limits over the last 30 years, despite the fact that the number of people reaching high age (say 95 years) was almost tripling. We also present estimates for the endpoints, for the force of mortality at very high age, and for the so-called perseverance parameter. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.7639697.v2
title: Inferring Atmospheric Release Characteristics in a Large Computer Experiment Using Bayesian Adaptive Splines

description: An atmospheric release of hazardous material, whether accidental or intentional, can be catastrophic for those in the path of the plume. Predicting the path of a plume based on characteristics of the release (location, amount, and duration) and meteorological conditions is an active research area highly relevant for emergency and long-term response to these releases. As a result, researchers have developed particle dispersion simulators to provide plume path predictions that incorporate release characteristics and meteorological conditions. However, since release characteristics and meteorological conditions are often unknown, the inverse problem is of great interest, that is, based on all the observations of the plume so far, what can be inferred about the release characteristics? This is the question we seek to answer using plume observations from a controlled release at the Diablo Canyon Nuclear Power Plant in Central California. With access to a large number of evaluations of a computationally expensive particle dispersion simulator that includes continuous and categorical inputs and spatio-temporal output, building a fast statistical surrogate model (or emulator) presents many statistical challenges, but is an essential tool for inverse modeling and sensitivity analysis. We achieve accurate emulation using Bayesian adaptive splines to model weights on empirical orthogonal functions. We use this emulator as well as appropriately identifiable simulator discrepancy and observational error models to calibrate the simulator, thus finding a posterior distribution of characteristics of the release. Since the release was controlled, these characteristics are known, making it possible to compare our findings to the truth. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.7445672.v3
title: Generalized Additive Models for Exceedances of High Thresholds With an Application to Return Level Estimation for U.S. Wind Gusts

description: Generalized additive model (GAM) forms offer a flexible approach to capturing marginal variation. Such forms are used here to represent distributional variation in extreme values and presented in terms of spatio-temporal variation, which is often evident in environmental processes. A two-stage procedure is proposed that identifies extreme values as exceedances of a high threshold, which is defined as a fixed quantile and estimated by quantile regression. Excesses of the threshold are modelled with the generalized Pareto distribution (GPD). GAM forms are adopted for the threshold and GPD parameters, and directly estimated—in particular smoothing parameters—by restricted maximum likelihood, which provides an objective and relatively fast method of inference. The GAM models are used to produce return level maps for extreme wind gust speeds over the United States, which show extreme quantiles of the distribution of annual maximum gust speeds. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.7823465.v3
title: A Hierarchical Framework for Correcting Under-Reporting in Count Data

description: Tuberculosis poses a global health risk and Brazil is among the top 20 countries by absolute mortality. However, this epidemiological burden is masked by under-reporting, which impairs planning for effective intervention. We present a comprehensive investigation and application of a Bayesian hierarchical approach to modeling and correcting under-reporting in tuberculosis counts, a general problem arising in observational count data. The framework is applicable to fully under-reported data, relying only on an informative prior distribution for the mean reporting rate to supplement the partial information in the data. Covariates are used to inform both the true count-generating process and the under-reporting mechanism, while also allowing for complex spatio-temporal structures. We present several sensitivity analyses based on simulation experiments to aid the elicitation of the prior distribution for the mean reporting rate and decisions relating to the inclusion of covariates. Both prior and posterior predictive model checking are presented, as well as a critical evaluation of the approach. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
DOI: 10.6084/m9.figshare.7757150.v2
title: Nonparametric Bayes Models of Fiber Curves Connecting Brain Regions

description: In studying structural inter-connections in the human brain, it is common to first estimate fiber bundles connecting different regions relying on diffusion MRI. These fiber bundles act as highways for neural activity. Current statistical methods reduce the rich information into an adjacency matrix, with the elements containing a count of fibers or a mean diffusion feature along the fibers. The goal of this article is to avoid discarding the rich geometric information of fibers, developing flexible models for characterizing the population distribution of fibers between brain regions of interest within and across different individuals. We start by decomposing each fiber into a rotation matrix, shape and translation from a global reference curve. These components are viewed as data lying on a product space composed of different Euclidean spaces and manifolds. To nonparametrically model the distribution within and across individuals, we rely on a hierarchical mixture of product kernels specific to the component spaces. Taking a Bayesian approach to inference, we develop efficient methods for posterior sampling. The approach automatically produces clusters of fibers within and across individuals. Applying the method to Human Connectome Project data, we find interesting relationships between brain fiber geometry and reading ability. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.