Wangli Xu

Model averaging, an effective method for reducing uncertainty in data modeling and learning, has been widely applied across various fields, including economics, finance, and operations research. The leave-one-out cross-validation (LOOCV) criterion is a widely used technique to choose weights in model averaging. It has achieved great success, but its application is limited by the high computational complexity, especially when the sample size is large. To address this issue, focusing on generalized linear models (GLMs), we propose a computationally efficient and approximate leave-one-out cross-validation (ALOOCV) weight choice criterion, which no longer suffers from the need to repeatedly solve optimization problems many times. Our theoretical analysis presents the discrepancy between the weight estimators produced by LOOCV and ALOOCV, which has been proven to vanish asymptotically under certain conditions. Moreover, the efficient jackknife model averaging (EJMA) procedure with ALOOCV for GLMs is proposed. The asymptotic optimality under the model misspecification and the convergence rate of the selected weights by ALOOCV are derived, and the over-consistency of the weight estimators and the consistency of averaging coefficient estimators are established if there exists at least one correct model. Additionally, to reduce the computational burden caused by an excessive number of candidate models, we provide a model screening procedure. Numerical experiments show the remarkable computational efficiency exhibited by EJMA relative to the model averaging procedure with LOOCV and the excellent prediction performance of our method over some common model averaging and selection procedures. History: Accepted by Ram Ramesh/Data Science & Machine Learning. Funding: This research was supported by the Postdoctoral Fellowship Program of CPSF [Grant GZC20231478], the National Natural Science Foundation of China [Grants 12501370, 12001534, and 12571300], and the China Postdoctoral Science Foundation [Grant 2024M761782]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0946 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0946 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Model averaging, an effective method for reducing uncertainty in data modeling and learning, has been widely applied across various fields, including economics, finance, and operations research. The leave-one-out cross-validation (LOOCV) criterion is a widely used technique to choose weights in model averaging. It has achieved great success, but its application is limited by the high computational complexity especially when the sample size is large. To address this issue, focusing on generalized linear models (GLMs), we propose a computationally efficient and approximate leave-one-out cross-validation (ALOOCV) weight choice criterion, which no longer suffers from the need to repeatedly solving optimization problems many times. Our theoretical analysis presents the discrepancy between the weight estimators produced by LOOCV and ALOOCV which is proved to vanish asymptotically under certain conditions. Moreover, the efficient jackknife model averaging (EJMA) procedure with ALOOCV for GLMs is proposed. The asymptotic optimality under the model misspecification and the convergence rate of the selected weights by ALOOCV are derived. And the over-consistency of the weight estimators and the consistency of averaging coefficient estimators are established if there exists at least one correct model. Additionally, to reduce the computational burden caused by an excessive number of candidate models, we provide a model screening procedure. Numerical experiments show the remarkable computational efficiency exhibited by EJMA relative to the model averaging procedure with LOOCV and the excellent prediction performance of our method over some common model averaging and selection procedures.

Hypothesis testing for fixed effects in linear mixed model is indispensable for investigating the utility of the predictors on response. However, when the dimension of covariates exceeds the sample size, the conventional frequentist methods designed for fixed dimensions fail completely. In this article, we develop a Bayesian‐motivated test for high‐dimensional linear mixed model to examine the significance of fixed effects in group. The proposed statistic is formulated as the ratio of two quadratic forms constructed from a sequence of independent but not identically distributed random variables. The null distribution of the proposed test statistic is derived through normality approximation for quadratic forms. To facilitate the implementation of the test, we introduce an innovative one‐step iteration method to determine the critical value. Additionally, the power function under local alternatives is derived under some mild conditions. In numerical experiments, we demonstrate the power performance in comparison with the existing method and the practical utility of the proposed method.

As a growing number of problems involve variables that are random objects, the development of models for such data has become increasingly important. This paper introduces a novel varying-coefficient Fréchet regression model that extends the classical varying-coefficient framework to accommodate random objects as responses. The proposed model provides a unified methodology for analyzing both Euclidean and non-Euclidean response variables. We develop a comprehensive estimation procedure that accommodates diverse predictor settings. Specifically, the model allows the effect-modifier variable U to be either Euclidean or non-Euclidean, while the predictors X are assumed to be Euclidean. Tailored estimation methods are provided for each scenario. To examine the asymptotic properties of the estimators, we introduce a smoothed version of the model and establish convergence rates through separate theoretical analyses of the bias and stochastic terms. The effectiveness and practical utility of the proposed methodology are demonstrated through extensive simulation studies and a real-data application.

This article proposes a calibrated empirical likelihood test for ultra-high dimensional means that incorporates multiple projections. Under weak moment conditions on the distributions of data, we analyse all possible asymptotic distributions of the proposed test statistic in different scenarios. To determine the critical value and enhance test power, we employ the random symmetrization method based on the group of sign flips and use multiple selected projections. The test can still maintain the significance level asymptotically, even in the presence of heterogeneity in the data distribution. Moreover, the proposed test procedure allows for general covariance structures and ultra-high dimensional regimes. Further, the power function reveals the relation with the projection term in an asymptotic sense such that we can select suitable projections to achieve good power in various scenarios. A quasi-Newton algorithm is introduced to reduce the computational cost arising from the intensive optimizations required for computing empirical likelihood. Numerical studies evidence the promising performance of the proposed test compared with existing tests.

Interaction selection for linear regression is useful in many fields of modern science, yet very challenging. Existing methods focus on finding one optimal model but they may perform poorly in terms of stability for high-dimensional data, and they do not typically deal with categorical predictors. In this paper, we introduce a variable importance based interaction modelling (VIBIM) procedure for learning interactions in a linear regression model with both continuous and categorical predictors. We apply the VIBIM procedure to a COVID-19 data and show that the VIBIM approach leads to better models in terms of interpretability, stability, reliability, and prediction.

Background. Over the past two decades, scarlet fever has resurged in some countries or areas. Nationwide nonpharmaceutical interventions changed the patterns of other infectious diseases, but its effects on the spread of scarlet fever were rarely studied. This study aimed to evaluate the changes in scarlet fever incidence in Zhejiang Province, China, before and during the COVID‐19 pandemic periods and to provide references for scarlet fever prevention and control. Methods. Scarlet fever surveillance data in Zhejiang, China (2004–2022), were analyzed in three stages. Two‐sample z test, ANOVA, and Tukey’s test were used to compare and analyze the characteristics of disease spread at different stages. The ARIMA model was used to predict the overall trend. The data were obtained from the National Infectious Disease Reporting Information System. Results. A total of 28,652 cases of scarlet fever were reported across Zhejiang Province during the study period, with the lowest average monthly incidences in 2020 (0.111/100,000). The predominant areas affected were the northern and central regions of Zhejiang, and all regions of Zhejiang experienced a decrease in incidence in 2020. The steepest decline in incidence in 2020 was found in children aged 0–4 years (67.3% decrease from 23.8/100,000 to 7.8/100,000). The seasonal pattern changed, with peak occurrences in April to June and November to January during 2004–2019 and 2021 and a peak in January in 2020. The median duration from diagnosis to confirmation was highest before COVID‐19 (4 days); however, it decreased to 1 day in 2020–2022, matching the other two medians. Conclusions. In 2020, Zhejiang experienced an unprecedented decrease in scarlet fever, with the lowest incidence in nearly 18 years, but it rebounded in 2021 and 2022. The seasonal epidemiologic characteristics of scarlet fever also changed with the COVID‐19 outbreaks. This suggested that nationwide nonpharmaceutical interventions greatly depressed the spread of scarlet fever. With the relaxation of non‐pharmaceutical intervention restrictions, scarlet fever may reappear. Government policymakers should prioritize the control of future scarlet fever outbreaks for public health.