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Comparisons of cognitive processing in monolinguals and bilinguals have revealed a bilingual advantage in inhibitory control. Recent studies have demonstrated advantages associated with exposure to two languages in infancy. However, the domain specificity and scope of the infant bilingual advantage in infancy remains unclear. In the present study, 114 monolingual and bilingual infants were compared in a very basic task of information processing—visual habituation—at 6 months of age. Bilingual infants demonstrated greater efficiency in stimulus encoding as well as in improved recognition memory for familiar stimuli as compared to monolinguals. Findings reveal a generalized cognitive advantage in bilingual infants that is broad in scope, early to emerge, and not specific to language.

Large covariance or correlation matrix is frequently assumed to be sparse in that a number of the off-diagonal elements of the matrix are zero. This paper focuses on estimating the sparsity of a large population covariance matrix using a sample correlation matrix under multivariate normal assumptions. We show that sparsity of a population covariance matrix can be well estimated by thresholding the sample correlation matrix. We then propose an empirical estimator for the sparsity and show that it is closely related to the thresholding methods. Upper bounds for the estimation error of the empirical estimator are given under mild conditions. Simulation shows that the empirical estimator can have smaller mean absolute errors than its main competitors. Furthermore, when the dimension of the covariance matrix is very large, we propose a generalized empirical estimator using simple random sampling. It is shown that the generalized empirical estimator can still estimate the sparsity well while the computation complexity can be greatly reduced.

Older adults have been reported to be a population with high-risk of death in the COVID-19 outbreak. Rapid detection of high-risk patients is crucial to reduce mortality in this population. The aim of this study was to evaluate the prognositc accuracy of the Modified Early Warning Score (MEWS) for in-hospital mortality in older adults with COVID-19. A retrospective cohort study was conducted in Wuhan Hankou Hospital in China from 1 January 2020 to 29 February 2020. Receiver operating characteristic (ROC) analysis was used to evaluate the predictive value of MEWS, Acute Physiology and Chronic Health Evaluation II (APACHE II), Sequential Organ Function Assessment (SOFA), quick Sequential Organ Function Assessment (qSOFA), Pneumonia Severity Index (PSI), Combination of Confusion, Urea, Respiratory Rate, Blood Pressure, and Age ≥65 (CURB-65), and the Systemic Inflammatory Response Syndrome Criteria (SIRS) for in-hospital mortality. Logistic regression models were performed to detect the high-risk older adults with COVID-19. Among the 235 patients included in this study, 37 (15.74%) died and 131 (55.74%) were male, with an average age of 70.61 years (SD 8.02). ROC analysis suggested that the capacity of MEWS in predicting in-hospital mortality was as good as the APACHE II, SOFA, PSI and qSOFA (Difference in AUROC: MEWS vs. APACHE II, -0.025 (95% CI [-0.075 to 0.026]); MEWS vs. SOFA, -0.013 (95% CI [-0.049 to 0.024]); MEWS vs. PSI, -0.015 (95% CI [-0.065 to 0.035]); MEWS vs. qSOFA, 0.024 (95% CI [-0.029 to 0.076]), all > 0.05), but was significantly higher than SIRS and CURB-65 (Difference in AUROC: MEWS vs. SIRS, 0.218 (95% CI [0.156-0.279]); MEWS vs. CURB-65, 0.064 (95% CI [0.002-0.125]), all < 0.05). Logistic regression models implied that the male patients (≥75 years) had higher risk of death than the other older adults (estimated coefficients: 1.16, = 0.044). Our analysis further suggests that the cut-off points of the MEWS score for the male patients (≥75 years) subpopulation and the other elderly patients should be 2.5 and 3.5, respectively. MEWS is an efficient tool for rapid assessment of elderly COVID-19 patients. MEWS has promising performance in predicting in-hospital mortality and identifying the high-risk group in elderly patients with COVID-19.

This article proposes a method of moments technique for estimating the sparsity of signals in a random sample. This involves estimating the largest eigenvalue of a large Hermitian trigonometric matrix under mild conditions. As illustration, the method is applied to two well-known problems. The first focuses on the sparsity of a large covariance matrix and the second investigates the sparsity of a sequence of signals observed with stationary, weakly dependent noise. Simulation shows that the proposed estimators can have significantly smaller mean absolute errors than their main competitors.

Quadratic regressions extend linear models by simultaneously including the main effects and the interactions between the covariates. As such, estimating interactions in high-dimensional quadratic regressions has received extensive attention. Here, we introduce a novel method that allows us to estimate the main effects and the interactions separately. Unlike existing methods for ultrahigh-dimensional quadratic regressions, our proposal does not require the widely used heredity assumption. In addition, our proposed estimates have explicit formulae and obey the invariance principle at the population level. We estimate the interactions in matrix form under a penalized convex loss function. The resulting estimates are shown to be consistent, even when the covariate dimension is an exponential order of the sample size. We develop an efficient alternating direction method of multipliers algorithm to implement the penalized estimation. This algorithm fully exploits the cheap computational cost of the matrix multiplication and is much more efficient than existing penalized methods, such as the all-pairs LASSO. We demonstrate the promising performance of the proposed method using extensive numerical studies.

Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this article, we rigorously study a directed network model that captures the former via node-specific parameterization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each node by different parameters, thus allowing the number of heterogeneity parameters to be twice the number of nodes. We study the maximum likelihood estimation of the model and establish the uniform consistency and asymptotic normality of the resulting estimators. Numerical studies demonstrate our theoretical findings and two data analyses confirm the usefulness of our model. Supplementary materials for this article are available online.

Reducing the bias of kernel density estimators has been a classical topic in nonparametric statistics. Schucany and Sommers (1977) proposed a two-scale estimator which cancelled the lower order bias by subtracting an additional kernel density estimator with a different scale of bandwidth. Different from existing literatures that treat the scale parameter in the two-scale estimator as a static global parameter, in this paper we consider an adaptive scale (i.e., dependent on the data point) so that the theoretical mean squared error can be further reduced. Practically, both the bandwidth and the scale parameter would require tuning, using for example, cross validation. By minimizing the point-wise mean squared error, we derive an approximate equation for the optimal scale parameter, and correspondingly propose to determine the scale parameter by solving an estimated equation. As a result, the only parameter that requires tuning using cross validation is the bandwidth. Point-wise consistency of the proposed estimator for the optimal scale is established with further discussions. The promising performance of the two-scale estimator based on the adaptive variable scale is illustrated via numerical studies on density functions with different shapes.

High-throughput profiling is now common in biomedical research. In this paper we consider the layout of an etiology study composed of a failure time response, and gene expression measurements. In current practice, a widely adopted approach is to select genes according to a preliminary marginal screening and a follow-up penalized regression for model building. Confounders, including for example clinical risk factors and environmental exposures, usually exist and need to be properly accounted for. We propose covariate-adjusted screening and variable selection procedures under the accelerated failure time model. While penalizing the high-dimensional coefficients to achieve parsimonious model forms, our procedure also properly adjust the low-dimensional confounder effects to achieve more accurate estimation of regression coefficients. We establish the asymptotic properties of our proposed methods and carry out simulation studies to assess the finite sample performance. Our methods are illustrated with a real gene expression data analysis where proper adjustment of confounders produces more meaningful results.

Estimating optimal individualized treatment rules (ITRs) in single- or multi-stage clinical trials is a key element of personalized medicine and, as a result, is receiving increasing attention within the statistical community. Recent works have suggested that machine learning approaches can provide significantly better estimations than those of model-based methods. However, a proper inference for estimated ITRs has not been well established for machine learning-based approaches. In this paper, we propose an entropy learning approach for estimating optimal ITRs. We obtain the asymptotic distributions for the estimated rules in order to provide a valid inference. The proposed approach is demonstrated to perform well through extensive simulation studies. Finally, we analyze data from a multi-stage clinical trial for depression patients. Our results offer novel findings not revealed by existing approaches.