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We generalize the sign covariance introduced by Bergsma & Dassios (2014) to multivariate random variables and beyond. The new interpoint-ranking sign covariance is applicable to general types of random objects as long as a meaningful similarity measure can be defined, and it is shown to be zero if and only if the two random variables are independent. The test statistic is a |$U$| -statistic, whose large-sample behaviour guarantees that the proposed test is consistent against general types of alternatives. Numerical experiments and data analyses demonstrate the superior empirical performance of the proposed method. [ABSTRACT FROM AUTHOR]

We consider multi-layer network data where the relationships between pairs of elements are reflected in multiple modalities, and may be described by multivariate or even high-dimensional vectors. Under the multi-layer stochastic block model framework we derive consistency results for a least squares estimation of memberships. Our theorems show that, as compared to single-layer community detection, a multi-layer network provides much richer information that allows for consistent community detection from a much sparser network, with required edge density reduced by a factor of the square root of the number of layers. Moreover, the multi-layer framework can detect cohesive community structure across layers, which might be hard to detect by any single-layer or simple aggregation. Simulations and a data example are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper concerns the modelling of multi-way functional data where double or multiple indices are involved. We introduce a concept of weak separability. The weakly separable structure supports the use of factorization methods that decompose the signal into its spatial and temporal components. The analysis reveals interesting connections to the usual strongly separable covariance structure, and provides insights into tensor methods for multi-way functional data. We propose a formal test for the weak separability hypothesis, where the asymptotic null distribution of the test statistic is a chi-squared-type mixture. The method is applied to study brain functional connectivity derived from source localized magnetoencephalography signals during motor tasks. [ABSTRACT FROM AUTHOR]

We introduce a simple and interpretable model for functional data analysis for situations where the observations at each location are functional rather than scalar. This new approach is based on a tensor product representation of the function-valued process and utilizes eigenfunctions of marginal kernels. The resulting marginal principal components and product principal components are shown to have nice properties. Given a sample of independent realizations of the underlying function-valued stochastic process, we propose straightforward fitting methods to obtain the components of this model and to establish asymptotic consistency and rates of convergence for the estimates proposed. The methods are illustrated by modelling the dynamics of annual fertility profile functions for 17 countries. This analysis demonstrates that the approach proposed leads to insightful interpretations of the model components and interesting conclusions. [ABSTRACT FROM AUTHOR]

Summary. Motivated by the conditional growth charts problem, we develop a method for conditional quantile analysis when predictors take values in a functional space. The method proposed aims at estimating conditional distribution functions under a generalized functional regression framework. This approach facilitates balancing of model flexibility and the curse of dimensionality for the infinite dimensional functional predictors. Its good performance in comparison with other methods, both for sparsely and for densely observed functional covariates, is demonstrated through theory as well as in simulations and an application to growth curves, where the method proposed can, for example, be used to assess the entire growth pattern of a child by relating it to the predicted quantiles of adult height. [ABSTRACT FROM AUTHOR]