Biometrika最新文献

We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a post-selection inference approach to canonical correlation analysis. The challenge is to adjust for the selection of subsets of variables having linear combinations with maximal sample correlation. To this end, we construct a stabilized one-step estimator of the euclidean-norm of the canonical correlations maximized over subsets of variables of pre-specified cardinality. This estimator is shown to be consistent for its target parameter and asymptotically normal, provided the dimensions of the variables do not grow too quickly with sample size. We also develop a greedy search algorithm to accurately compute the estimator, leading to a computationally tractable omnibus test for the global null hypothesis that there are no linear relationships between any subsets of variables having the pre-specified cardinality. We further develop a confidence interval that takes the variable selection into account.

This paper develops a functional hybrid factor regression modelling framework to handle the heterogeneity of many large-scale imaging studies, such as the Alzheimer's disease neuroimaging initiative study. Despite the numerous successes of those imaging studies, such heterogeneity may be caused by the differences in study environment, population, design, protocols or other hidden factors, and it has posed major challenges in integrative analysis of imaging data collected from multicentres or multistudies. We propose both estimation and inference procedures for estimating unknown parameters and detecting unknown factors under our new model. The asymptotic properties of both estimation and inference procedures are systematically investigated. The finite-sample performance of our proposed procedures is assessed by using Monte Carlo simulations and a real data example on hippocampal surface data from the Alzheimer's disease study.

This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes the distance from the covariance estimate to a symmetric sparsity set. This formulation avoids unwanted shrinkage induced by more common norm penalties, and enables optimization of the resulting nonconvex objective by solving a sequence of smooth, unconstrained subproblems. These subproblems are generated and solved via the proximal distance version of the majorization-minimization principle. The resulting algorithm executes rapidly, gracefully handles settings where the number of parameters exceeds the number of cases, yields a positive-definite solution, and enjoys desirable convergence properties. Empirically, we demonstrate that our approach outperforms competing methods across several metrics, for a suite of simulated experiments. Its merits are illustrated on international migration data and a case study on flow cytometry. Our findings suggest that the marginal and conditional dependency networks for the cell signalling data are more similar than previously concluded.

For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is undesirable, especially for highly multivariate settings, where popular cross-covariance functions such as the multivariate Matérn suffer from a "curse of dimensionality" as the number of parameters and floating point operations scale up in quadratic and cubic order, respectively, in the number of variables. We propose a class of multivariate "Graphical Gaussian Processes" using a general construction called "stitching" that crafts cross-covariance functions from graphs and ensures process-level conditional independence among variables. For the Matérn family of functions, stitching yields a multivariate GP whose univariate components are Matérn GPs, and conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Matérn GP to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling.