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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 models.This 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 error.Simulation studies are conducted to evaluate the performance of the proposed method and compare it with the competitors to demonstrate its superiority.The 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 University School of Chinese Materia Medica Beijing University of Chinese Medicine

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

asymptotic optimality of the Nonnegative Garrote Estimator Under Heteroscedastic Errors

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Journal of Systems Science & Complexity 2020年第2期33卷 545-562页

作者： CHEN Xiuping CAI Guanghui GAO Yan ZHAO Shangwei College of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China Department of Statistics College of ScienceMinzu University of ChinaBeijing 100081China

This paper proposes the Nonnegative Garrote(NG)estimator for linear model with heteroscedastic errors.On the other hand,under some regularity conditions,the authors show the asymptotic optimality of the NG estimator by referring to the idea of the asymptotic optimality of the model average estimator.Simulation results and a real data analysis are reported for testing the results obtained previously.These results provide a stronger theoretical basis for the use of NG estimator by strengthening existing findings.

关键词： asymptotic optimality coefficient shrinkage heteroscedastic errors Nonnegative Garrote

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

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 weights.In 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(∞))process.Under 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 prediction.Simulations 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 size.Under model misspecification,the asymptotic optimality is derived in the sense of achieving the lowest possible squared errors.The 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 performance.The 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

Least Squares Model Averaging for Two Non-Nested Linear Models

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Journal of Systems Science & Complexity 2023年第1期36卷 412-432页

作者： GAO Yan XIE Tianfa ZOU Guohua Department of Statistics College of ScienceMinzu University of ChinaBeijing 100081China Faculty of Science Beijing University of TechnologyBeijing 100124China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

This paper studies the least squares model averaging methods for two non-nested linear models.It is proved that the Mallows model averaging weight of the true model is root-n consistent.Then the authors develop a penalized Mallows criterion which ensures that the weight of the true model equals 1 with probability tending to 1 and thus the averaging estimator is asymptotically normal.If neither candidate model is true,the penalized Mallows averaging estimator is asymptotically optimal.Simulation results show the selection consistency of the penalized Mallows method and the superiority of the model averaging approach compared with the model selection estimation.

关键词： asymptotic optimality consistency least squares model averaging non-nested models

Mallows Model Averaging Estimation for Linear Regression Model with Right Censored Data

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 5-23页

作者： Zhong-qi LIANG Xiao-lin CHEN Yan-qiu ZHOU School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China School of Statistics Qufu Normal UniversityQufu 273165China School of Science Guangxi University of Science and TechnologyLiuzhou 545006China

This paper is concerned with an optimal model averaging estimation for linear regression model with right censored data. The weights for model averaging are picked up via minimizing the Mallows criterion. Under some mild conditions, it is shown that the identified weights possess the property of asymptotic optimality, that is,the model averaging estimator corresponding to these weights achieves the lowest squared error asymptotically.Some numerical studies are conducted to evaluate the finite-sample performance of our method and make comparisons with its intuitive competitors, while an application to the PBC dataset is provided to serve as an illustration.

关键词： model averaging right censoring asymptotic optimality synthetic data