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The aim of this paper is to conduct a systematic and theoretical analysis of estimation and inference for a class of functional mixed effects models (FMEM). Such FMEMs consist of fixed effects that characterize the association between longitudinal functional responses and covariates of interest and random effects that capture the spatial-temporal correlations of longitudinal functional responses. We propose local linear estimates of refined fixed effect functions and establish their weak convergence along with a simultaneous confidence band for each fixed-effect function. We propose a global test for the linear hypotheses of varying coefficient functions and derive the associated asymptotic distribution under the null hypothesis and the asymptotic power under the alternative hypothesis are derived. We also establish the convergence rates of the estimated spatial-temporal covariance operators and their associated eigenvalues and eigenfunctions. We conduct extensive simulations and apply our method to a white-matter fiber data set from a national database for autism research to examine the finite-sample performance of the proposed estimation and inference procedures.

Hypotheses exploring the influence of dietary conditions on the life history trade-off between survival and reproductive success are extensively tested in female insects, but are rarely explored in males. Here, the impact of dietary quality and female access on age-specific reproduction and survival of male Mexican fruit flies, Anastrepha ludens Loew (Diptera: Tephritidae), are examined. There is a clear cost of female access for males with access to dietary protein, measurable as a decrease in life expectancy, which is further influenced by the age when females are introduced. A protein deficient diet reduces the lifespan benefit of virginity and masks the detrimental effect of female access on male life expectancy. Dietary protein is not necessary for reproductive success, but access to protein at eclosion improves the lifetime reproductive success of males compared to when it is delayed. Overall, reproductive success diminishes as the male flies age, regardless of the dietary conditions, providing evidence for reproductive senescence in males. Delaying the males' access to a protein source fails to influence the negative effect of age on reproductive ability. Because age specific reproductive rates decline with age, regardless of diet, male fitness does not benefit from lifespan extension. Therefore, males can be expected to allocate available resources towards reproductive effort in favour of extended lifespan, regardless of mate and protein availability.

Many longitudinal imaging studies have collected repeated diffusion tensor magnetic resonance imaging data to understand white matter maturation and structural connectivity pattern in normal controls and diseased subjects. There is an urgent demand for the development of statistical methods for the analysis of diffusion properties along fiber tracts and clinical data obtained from longitudinal studies. Jointly analyzing repeated fiber-tract diffusion properties and covariates (e.g., age or gender) raises several major challenges including (i) infinite-dimensional functional response data, (ii) complex spatial-temporal correlation structure, and (iii) complex spatial smoothness. To address these challenges, this article is to develop a functional mixed effects modeling (FMEM) framework to delineate the dynamic changes of diffusion properties along major fiber tracts and their association with a set of covariates of interest and the structure of the variability of these white matter tract properties in various longitudinal studies. Our FMEM consists of a functional mixed effects model for addressing all three challenges, an efficient method for spatially smoothing varying coefficient functions, an estimation method for estimating the spatial-temporal correlation structure, a test procedure with local and global test statistics for testing hypotheses of interest associated with functional response, and a simultaneous confidence band for quantifying the uncertainty in the estimated coefficient functions. Simulated data are used to evaluate the finite sample performance of FMEM and to demonstrate that FMEM significantly outperforms the standard pointwise mixed effects modeling approach. We apply FMEM to study the spatial-temporal dynamics of white-matter fiber tracts in a clinical study of neurodevelopment.

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]

Background: Postmortem human brain studies provide the molecular, cellular, and circuitry levels of resolution essential for the development of mechanistically-novel interventions for cognitive deficits in schizophrenia. However, the absence of measures of premortem cognitive aptitude in postmortem subjects has presented a major challenge to interpreting the relationship between the severity of neural alterations and cognitive deficits within the same subjects. Methods: To begin addressing this challenge, proxy measures of cognitive aptitude were evaluated in postmortem subjects (N = 507) meeting criteria for schizophrenia, major depressive or bipolar disorder, and unaffected comparison subjects. Specifically, highest levels of educational and occupational attainment of the decedent and their parents were obtained during postmortem psychological autopsies. Results: Consistent with prior findings in living subjects, subjects with schizophrenia had the lowest educational and occupational attainment relative to all other subject groups, and they also failed to show the generational improvement in attainment observed in all other subject groups. Conclusions: Educational and occupational attainment data obtained during postmortem psychological autopsies can be used as proxy measures of premortem cognitive function to interrogate the neural substrate of cognitive dysfunction in schizophrenia. [ABSTRACT FROM AUTHOR]