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The covariance matrix associated with multiple financial returns plays foundational roles in many empirical applications, for example, quantifying risks and managing investment portfolios. Such covariance matrices are well known to be dynamic, that is, their structures change with the underlying market conditions. To incorporate such dynamics in a setting with high-frequency noisy data contaminated by measurement errors, we propose a new approach for estimating the covariances of a high-dimensional return series. By utilizing an appropriate localization, our approach is designed upon exploiting generic variables that are informative in accounting for the dynamic changes. We then investigate the properties and performance of the high-dimensional minimal-variance sparse portfolio constructed from employing the proposed dynamic covariance estimator. Our theory establishes the validity of the proposed covariance estimation methods in handling high-dimensional, high-frequency noisy data. The promising applications of our methods are demonstrated by extensive simulations and empirical studies showing the satisfactory accuracy of the covariance estimation and the substantially improved portfolio performance.

Recent technological advances have made it possible to collect high-dimensional genomic data along with clinical data on a large number of subjects. In the studies of chronic diseases such as cancer, it is of great interest to integrate clinical and genomic data to build a comprehensive understanding of the disease mechanisms. Despite extensive studies on integrative analysis, it remains an ongoing challenge to model the interaction effects between clinical and genomic variables, due to high dimensionality of the data and heterogeneity across data types. In this paper, we propose an integrative approach that models interaction effects using a single-index varying-coefficient model, where the effects of genomic features can be modified by clinical variables. We propose a penalized approach for separate selection of main and interaction effects. Notably, the proposed methods can be applied to right-censored survival outcomes based on a Cox proportional hazards model. We demonstrate the advantages of the proposed methods through extensive simulation studies and provide applications to a motivating cancer genomic study.

Quadratic regression goes beyond the linear model by simultaneously including main effects and interactions between the covariates. The problem of interaction estimation in high dimensional quadratic regression has received extensive attention in the past decade. In this article we introduce a novel method which allows us to estimate the main effects and 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 formulas and obey the invariance principle at the population level. We estimate the interactions of matrix form under 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 ADMM algorithm to implement the penalized estimation. This ADMM algorithm fully explores the cheap computational cost of matrix multiplication and is much more efficient than existing penalized methods such as all pairs LASSO. We demonstrate the promising performance of our proposal through extensive numerical studies., Comment: 33 pages, 2 figures and 3 tables

Background 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. Methods 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. Results 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 P > 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 P < 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, P = 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. Conclusions 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.

High-dimensional data that evolve dynamically feature predominantly in the modern data era. As a partial response to this, recent years have seen increasing emphasis to address the dimensionality challenge. However, the non-static nature of these datasets is largely ignored. This paper addresses both challenges by proposing a novel yet simple dynamic linear programming discriminant (DLPD) rule for binary classification. Different from the usual static linear discriminant analysis, the new method is able to capture the changing distributions of the underlying populations by modeling their means and covariances as smooth functions of covariates of interest. Under an approximate sparse condition, we show that the conditional misclassification rate of the DLPD rule converges to the Bayes risk in probability uniformly over the range of the variables used for modeling the dynamics, when the dimensionality is allowed to grow exponentially with the sample size. The minimax lower bound of the estimation of the Bayes risk is also established, implying that the misclassification rate of our proposed rule is minimax-rate optimal. The promising performance of the DLPD rule is illustrated via extensive simulation studies and the analysis of a breast cancer dataset., Comment: 34 pages; 3 figures

We consider sample size calculation to obtain sufficient estimation precision and control the length of confidence intervals under high dimensional assumptions. In particular, we intend to provide more general results for sample size determination when a large number of parameter values need to be computed for a fixed sample. We consider three design approaches: normal approximation, inequality method and regression method. These approaches are applied to sample size calculation in estimating the Net Reclassification Improvement (NRI) and the Integrated Discrimination Improvement (IDI) for a diagnostic or screening study. Two medical examples are also provided as illustration. Our results suggest the regression method in general can yield a much smaller sample size than other methods.

Instrumental variable (IV) methods are popular in non-experimental settings to estimate the causal effects of scientific interventions. These approaches allow for the consistent estimation of treat...

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 paper, we propose a new directed network model to capture the former via node-specific parametrization 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 a data analysis confirms the usefulness of our model., Comment: 29 pages. minor revision

We propose a semiparametric linear programming discriminant (SLPD) rule for high dimensional discriminant analysis under a semiparametric model. As an extension, we further propose a two-stage SLPD (TSLPD) rule, which can have better classification performance under mild sparsity assumptions.

The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to solve problems with a very large $p$. In this paper, we propose a very efficient algorithm for precision matrix estimation via penalized quadratic loss functions. Under the high dimension low sample size setting, the computation complexity of our algorithm is linear in both the sample size and the number of parameters. Such a computation complexity is in some sense optimal, as it is the same as the complexity needed for computing the sample covariance matrix. Numerical studies show that our algorithm is much more efficient than other state-of-the-art methods when the dimension $p$ is very large., 18 pages, 2 tables and 3 figures

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 paper, we rigorously study a directed network model that captures the former via node-specific parametrization 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.

This paper studies the dimension effect of the linear discriminant analysis (LDA) and the regularized linear discriminant analysis (RLDA) classifiers for large dimensional data where the observation dimension $p$ is of the same order as the sample size $n$. More specifically, built on properties of the Wishart distribution and recent results in random matrix theory, we derive explicit expressions for the asymptotic misclassification errors of LDA and RLDA respectively, from which we gain insights of how dimension affects the performance of classification and in what sense. Motivated by these results, we propose adjusted classifiers by correcting the bias brought by the unequal sample sizes. The bias-corrected LDA and RLDA classifiers are shown to have smaller misclassification rates than LDA and RLDA respectively. Several interesting examples are discussed in detail and the theoretical results on dimension effect are illustrated via extensive simulation studies., 34pages,6figures

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.

This article shows that when the nonzero coefficients of the population correlation matrix are all greater in absolute value than ( C 1 log p / n ) 1 / 2 for some constant C 1 , we can obtain covariance selection consistency by thresholding the sample correlation matrix. Furthermore, the rate ( log p / n ) 1 / 2 is shown to be optimal.

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. Copyright 2012, Oxford University Press.

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.

Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however, when the dimensionality is relatively large. To address this, we propose a novel procedure named DA-QDA for QDA in analyzing high-dimensional data. Formulated in a simple and coherent framework, DA-QDA aims to directly estimate the key quantities in the Bayes discriminant function including quadratic interactions and a linear index of the variables for classification. Under appropriate sparsity assumptions, we establish consistency results for estimating the interactions and the linear index, and further demonstrate that the misclassification rate of our procedure converges to the optimal Bayes risk, even when the dimensionality is exponentially high with respect to the sample size. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed for finding interactions, which is much faster than its competitor in the literature. The promising performance of DA-QDA is illustrated via extensive simulation studies and the analysis of four real datasets., Comment: Updated to the JMLR format

In this paper, we extend the definitions of the net reclassification improvement (NRI) and the integrated discrimination improvement (IDI) in the context of multicategory classification. Both measures were proposed in Pencina and others (2008. Evaluating the added predictive ability of a new marker: from area under the receiver operating characteristic (ROC) curve to reclassification and beyond. Statistics in Medicine 27, 157–172) as numeric characterizations of accuracy improvement for binary diagnostic tests and were shown to have certain advantage over analyses based on ROC curves or other regression approaches. Estimation and inference procedures for the multiclass NRI and IDI are provided in this paper along with necessary asymptotic distributional results. Simulations are conducted to study the finite-sample properties of the proposed estimators. Two medical examples are considered to illustrate our methodology.