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asymptotic optimality for consensus-type stochastic approximation algorithms using iterate averaging

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控制理论与应用（英文版） 2013年第1期11卷 1-9页

作者： Gang YIN Le Yi WANG Yu SUN David CASBEER Raymond HOLSAPPLE Derek KINGSTON Department of Mathematics Wayne State University Department of Electrical and Computer Engineering Wayne State University Quantitative Business Analysis Department Siena College Control Science Center of Excellence Air Force Research Laboratory

This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large stepsizes. Then, the second stage provides a refinement by averaging the iterates from the first stage. We show that the new algorithm is asymptotically efficient and gives the optimal convergence rates in the sense of the best scaling factor and ＇smallest＇ possible asymptotic variance.

关键词： Stochastic approximation algorithm Consensus Iterate averaging asymptotic optimality

Analyzing the Dissemination of News by Model Averaging and Subsampling

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Journal of Systems Science & Complexity 2024年第5期37卷 2104-2131页

作者： ZOU Jiahui School of Statistics Capital University of Economics and Business

The dissemination of news is a vital topic in management science, social science and data science. With the development of technology, the sample sizes and dimensions of digital news data increase remarkably. To alleviate the computational burden in big data, this paper proposes a method to deal with massive and moderate-dimensional data for linear regression models via combing model averaging and subsampling methodologies. The author first samples a subsample from the full data according to some special probabilities and split covariates into several groups to construct candidate models. Then, the author solves each candidate model and calculates the model-averaging weights to combine these estimators based on this subsample. Additionally, the asymptotic optimality in subsampling form is proved and the way to calculate optimal subsampling probabilities is *** author also illustrates the proposed method via simulations, which shows it takes less running time than that of the full data and generates more accurate estimations than uniform subsampling. Finally,the author applies the proposed method to analyze and predict the sharing number of news, and finds the topic, vocabulary and dissemination time are the determinants.

关键词： asymptotic optimality dissemination of news linear regression models model averaging optimal subsampling

Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method

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Journal of Systems Science & Complexity 2024年第5期37卷 2132-2156页

作者： FENG Ziheng ZONG Xianpeng XIE Tianfa ZHANG Xinyu School of Mathematics Statistics and Mechanics Beijing University of Technology Academy of Mathematics and Systems Science Chinese Academy of Sciences

In recent years, Kriging model has gained wide popularity in various fields such as space geology, econometrics, and computer experiments. As a result, research on this model has *** this paper, the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method, with consideration for the model uncertainty. The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method. First, the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction ***, the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models. The effectiveness of the proposed method is verified through numerical analyses.

关键词： asymptotic optimality best linear unbiased prediction cross-validation Kriging model model averaging

Partial Linear Model Averaging Prediction for Longitudinal Data

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Journal of Systems Science & Complexity 2024年第2期37卷 863-885页

作者： LI Na FEI Yu ZHANG Xinyu Faculty of Science Kunming University of Science and TechnologyKunming 650500China School of Statistics and Mathematics Yunnan University of Finance and EconomicsKunming 650221China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China

Prediction plays an important role in data *** averaging method generally provides better prediction than using any of its *** though model averaging has been extensively investigated under independent errors,few authors have considered model averaging for semiparametric models with correlated *** this paper,the authors offer an optimal model averaging method to improve the prediction in partially linear model for longitudinal *** model averaging weights are obtained by minimizing criterion,which is an unbiased estimator of the expected in-sample squared error loss plus a *** properties,including asymptotic optimality and consistency of averaging weights,are established under two scenarios:(i)All candidate models are misspecified;(ii)Correct models are available in the candidate *** studies and an empirical example show that the promise of the proposed procedure over other competitive methods.

关键词： asymptotic optimality longitudinal data model averaging estimator partially linear model prediction

Optimal Model Average Prediction in Orthogonal Kriging Models

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Journal of Systems Science & Complexity 2024年第3期37卷 1080-1099页

作者： WANG Jun HE Jiabei LIANG Hua LI Xinmin School of Mathematics and Statistics Qingdao UniversityQingdao 266071China Department of Statistics George Washington UniversityWashington DC 20052USA

The main objective of this paper is to consider model averaging methods for kriging *** paper proposes a Mallows model averaging procedure for the orthogonal kriging model and demonstrate the asymptotic optimality of the model averaging estimators in terms of mean square *** studies are conducted to evaluate the performance of the proposed method and compare it with the competitors to demonstrate its *** authors also analyse a real dataset for an illustration.

关键词： asymptotic optimality Mallows criterion optimal model averaging orthogonal kriging model

Jackknife Model Averaging for Composite Quantile Regression

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Journal of Systems Science & Complexity 2024年第4期37卷 1604-1637页

作者： YOU Kang WANG Miaomiao ZOU Guohua School of Mathematical Sciences Capital Normal UniversityBeijing 100089China School of Chinese Materia Medica Beijing University of Chinese MedicineBeijing 100105China

In this paper,the authors propose a frequentist model averaging method for composite quantile regression with diverging number of *** from the traditional model averaging for quantile regression which considers only a single quantile,the proposed model averaging estimator is based on multiple *** well-known delete-one cross-validation or jackknife approach is applied to estimate the model *** resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction *** studies are conducted to demonstrate the finite sample performance of the new model averaging *** proposed method is also applied to the analysis of the stock returns data and the wage data.

关键词： asymptotic optimality composite quantile regression cross-validation model averaging

Cross Validation Based Model Averaging for Varying-Coefficient Models with Response Missing at Random

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Journal of Applied Mathematics and Physics 2024年第3期12卷 764-777页

作者： Huixin Li Xiuli Wang School of Mathematics and Statistics Shandong Normal University Jinan China

In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.

关键词： Response Missing at Random Model Averaging asymptotic optimality B-Spline Approximation

Model Averaging Multistep Prediction in an Infinite Order Autoregressive Process

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Journal of Systems Science & Complexity 2022年第5期35卷 1875-1901页

作者： YUAN Huifang LIN Peng JIANG Tao XU Jinfeng School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China School of Mathematics and Statistics Zaozhuang UniversityZaozhuang 277000China School of Mathematics and Statistics Shandong University of TechnologyZibo 255000China Hangzhou College of Commerce Zhejiang Gongshang UniversityTonglu 311599China Department of Statistics and Actuarial Science The University of Hong KongHongKong 999077China

The key issue in the frequentist model averaging is the choice of *** this paper,the authors advocate an asymptotic framework of mean-squared prediction error(MSPE)and develop a model averaging criterion for multistep prediction in an infinite order autoregressive(AR(∞))*** the assumption that the order of the candidate model is bounded,this criterion is proved to be asymptotically optimal,in the sense of achieving the lowest out of sample MSPE for the samerealization *** and real data analysis further demonstrate the effectiveness and the efficiency of the theoretical results.

关键词： asymptotic optimality autoregressive process multistep prediction the same-realization prediction

Model Averaging Estimation for Varying-Coefficient Single-Index Models

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Journal of Systems Science & Complexity 2022年第1期35卷 264-282页

作者： LIU Yue ZOU Jiahui ZHAO Shangwei YANG Qinglong School of Statistics Jiangxi University of Finance and EconomicsNanchang 330013China. School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China. School of Science Minzu University of ChinaBeijing 100081China School of Statistics and Mathematics Zhongnan University of Economics and LawWuhan 430073China

The varying-coefficient single-index model(VCSIM)is widely used in economics,statistics and biology.A model averaging method for VCSIM based on a Mallows-type criterion is proposed to improve prodictive capacity,which allows the number of candidate models to diverge with sample *** model misspecification,the asymptotic optimality is derived in the sense of achieving the lowest possible squared *** authors compare the proposed model averaging method with several other classical model selection methods by simulations and the corresponding results show that the model averaging estimation has a outstanding *** authors also apply the method to a real dataset.

关键词： asymptotic optimality kernel-local smoothing method Mallows-type criterion model averaging varying-coefficient single-index model