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Motivated by image‐on‐scalar regression with data aggregated across multiple sites, we consider a setting in which multiple independent studies each collect multiple dependent vector outcomes, with potential mean model parameter homogeneity between studies and outcome vectors. To determine the validity of a joint analysis of these data sources, we must learn which of them share mean model parameters. We propose a new model fusion approach that delivers improved flexibility and statistical performance over existing methods. Our proposed approach specifies a quadratic inference function within each data source and fuses mean model parameter vectors in their entirety based on a new formulation of a pairwise fusion penalty. We establish theoretical properties of our estimator and propose an asymptotically equivalent weighted oracle meta‐estimator that is more computationally efficient. Simulations and an application to the ABIDE neuroimaging consortium highlight the flexibility of the proposed approach. An R package is provided for ease of implementation. [ABSTRACT FROM AUTHOR]

Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using Max Stable Processes (MSPs) that are computationally prohibitive to fit for as few as a dozen observations. Supposed computationally-efficient approaches like the composite likelihood remain computationally burdensome with a few hundred observations. In this article, we propose a spatial partitioning approach based on local modeling of subsets of the spatial domain that delivers computationally and statistically efficient inference. Marginal and dependence parameters of the MSP are estimated locally on subsets of observations using censored pairwise composite likelihood, and combined using a modified generalized method of moments procedure. The proposed distributed approach is extended to estimate inverted MSP models, and to estimate spatially varying coefficient models to deliver computationally efficient modeling of spatial variation in marginal parameters. We demonstrate consistency and asymptotic normality of estimators, and show empirically that our approach leads to statistically efficient estimation of model parameters. We illustrate the flexibility and practicability of our approach through simulations and the analysis of streamflow data from the U.S. Geological Survey. for this article are available online. [ABSTRACT FROM AUTHOR]

Modern longitudinal data, for example from wearable devices, may consist of measurements of biological signals on a fixed set of participants at a diverging number of time-points. Traditional statistical methods are not equipped to handle the computational burden of repeatedly analysing the cumulatively growing dataset each time new data are collected. We propose a new estimation and inference framework for dynamic updating of point estimates and their standard errors along sequentially collected datasets with dependence, both within and between the datasets. The key technique is a decomposition of the extended inference function vector of the quadratic inference function constructed over the cumulative longitudinal data into a sum of summary statistics over data batches. We show how this sum can be recursively updated without the need to access the whole dataset, resulting in a computationally efficient streaming procedure with minimal loss of statistical efficiency. We prove consistency and asymptotic normality of our streaming estimator as the number of data batches diverges, even as the number of independent participants remains fixed. Simulations demonstrate the advantages of our approach over traditional statistical methods that assume independence between data batches. Finally, we investigate the relationship between physical activity and several diseases through analysis of accelerometry data from the National Health and Nutrition Examination Survey. [ABSTRACT FROM AUTHOR]

This article is motivated by a regression analysis of electroencephalography (EEG) neuroimaging data with high-dimensional correlated responses with multilevel nested correlations. We develop a divide-and-conquer procedure implemented in a fully distributed and parallelized computational scheme for statistical estimation and inference of regression parameters. Despite significant efforts in the literature, the computational bottleneck associated with high-dimensional likelihoods prevents the scalability of existing methods. The proposed method addresses this challenge by dividing responses into subvectors to be analyzed separately and in parallel on a distributed platform using pairwise composite likelihood. Theoretical challenges related to combining results from dependent data are overcome in a statistically efficient way using a meta-estimator derived from Hansen's generalized method of moments. We provide a rigorous theoretical framework for efficient estimation, inference, and goodness-of-fit tests. We develop an R package for ease of implementation. We illustrate our method's performance with simulations and the analysis of the EEG data, and find that iron deficiency is significantly associated with two auditory recognition memory related potentials in the left parietal-occipital region of the brain. for this article are available online. [ABSTRACT FROM AUTHOR]

This paper presents a unified framework for supervised learning and inference procedures using the divide-and-conquer approach for high-dimensional correlated outcomes. We propose a general class of estimators that can be implemented in a fully distributed and parallelized computational scheme. Modeling, computational and theoretical challenges related to high-dimensional correlated outcomes are overcome by dividing data at both outcome and subject levels, estimating the parameter of interest from blocks of data using a broad class of supervised learning procedures, and combining block estimators in a closed-form meta-estimator asymptotically equivalent to estimates obtained by Hansen (1982)'s generalized method of moments (GMM) that does not require the entire data to be reloaded on a common server. We provide rigorous theoretical justifications for the use of distributed estimators with correlated outcomes by studying the asymptotic behaviour of the combined estimator with fixed and diverging number of data divisions. Simulations illustrate the finite sample performance of the proposed method, and we provide an R package for ease of implementation. [ABSTRACT FROM AUTHOR]