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Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression

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Journal of Systems Science & Complexity 2020年第2期33卷 527-544页

作者： YU Ping zhu zhongyi SHI Jianhong AI Xikai School of Mathematics and Computer Science Shanxi Normal UniversityLinfen 041000China Department of Statistics Fudan UniversityShanghai 200433China

This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression,which combines the common linear model with the functional linear regression *** outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error *** slope function is fitted by *** suitable conditions,the authors obtain the convergence rates and asymptotic normality of the ***,simulation studies and a real data example are conducted to examine the finite sample performance of the proposed *** the simulation results and the real data analysis confirm that the newly proposed method works very well.

关键词： B-spline functional data analysis functional linear model modal regression

Dynamic single-index model for functional data

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Science China Mathematics 2016年第12期59卷 2561-2584页

作者： MA HaiQiang BAI Yang zhu zhongyi Department of Statistics Fudan University Department of Mathematics Taiyuan University of Science and Technology School of Statistics and Management Shanghai University of Finance and Economics

We propose a new functional single index model, which called dynamic single-index model for functional data, or DSIM, to efficiently perform non-linear and dynamic relationships between functional predictor and functional response. The proposed model naturally allows for some curvature not captured by the ordinary functional linear model. By using the proposed two-step estimating algorithm, we develop the estimates for both the link function and the regression coefficient function, and then provide predictions of new response trajectories. Besides the asymptotic properties for the estimates of the unknown functions, we also establish the consistency of the predictions of new response trajectories under mild conditions. Finally, we show through extensive simulation studies and a real data example that the proposed DSIM can highly outperform existed functional regression methods in most settings.

关键词： functional data analysis dynamic single-index model local linear smoothing prediction

Variable selection in censored quantile regression with high dimensional data

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Science China Mathematics 2018年第4期61卷 641-658页

作者： Yali Fan Yanlin Tang zhongyi zhu College of Science University of Shanghai for Science and Technology School of Mathematical Sciences Tongji University Department of Statistics Fudan University

We propose a two-step variable selection procedure for censored quantile regression with high dimensional predictors. To account for censoring data in high dimensional case, we employ effective dimension reduction and the ideas of informative subset idea. Under some regularity conditions, we show that our procedure enjoys the model selection consistency. Simulation study and real data analysis are conducted to evaluate the finite sample performance of the proposed approach.

关键词： adaptive LASSO censoring high dimensional quantile regression

Joint semiparametric mean-covariance model in longitudinal study

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Science China Mathematics 2011年第1期54卷 145-164页

作者： MAO Jie zhu zhongyi Department of Statistics Fudan University Shanghai 200433 China

Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach.

关键词： generalized estimating equation kernel estimation local linear regression modified Cholesky decomposition semiparametric varying-coefficient partially linear model

ASYMPTOTIC EFFICIENT ESTIMATION IN SEMIPARAMETRIC NONLINEAR REGRESSION MODELS

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Applied Mathematics(A Journal of Chinese Universities) 1999年第1期14卷 57-66页

作者： zhu zhongyi\ Wei Bocheng Dept. of Appl. Math. Southeast Univ. Nanjing

Abstract In this paper, the estimation method based on the “generalized profile likelihood” for the conditionally parametric models in the paper given by Severini and Wong (1992) is extended to fixed design semiparametric nonlinear regression *** these semiparametric nonlinear regression models,the resulting estimator of parametric component of the model is shown to be asymptotically efficient and the strong convergence rate of nonparametric component is *** results (for example Chen (1988),Gao & Zhao (1993), Rice (1986) et al.) are extended to fixed design semiparametric nonlinear regression models.

关键词： 1991 MR Subject Classification 62G07 62F35

On the MLE of the Waring distribution

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Statistical Theory and Related Fields 2023年第2期7卷 144-158页

作者： Yanlin Tang Jinglong Wang zhongyi zhu KLATASDS-MOE School of StatisticsEast China Normal University ShanghaiPeople's Republic of China Department of Statistics and Data Science Fudan UniversityShanghaiPeople's Republic of China

The two-parameter Waring is an important heavy-tailed discrete distribution,which extends the famous Yule Simon distribution and provides more flexibility when modelling the *** commonly used EFF(Expectation-First Frequency)for parameter estimation can only be applied when the first moment exists,and it only uses the information of the expectation and the first frequency,which is not as efficient as the maximum likelihood estimator(MLE).However,the MLE may not exist for some sample *** apply the profle method to the log-likelihood function and derive the necessary and sufficient Conditions for the existence of the MLE of the Waring *** use extensive simulation studies to compare the MLE and EFF methods,and the goodness-of-fit comparison with the Yule Simon *** also apply the Waring distribution to fit an insurance data.

关键词： Maximum lkelihood estimator heay-tailed discrete distribution Waring distribution

ASYMPTOTIC PROPERTIES OF MLE IN EXPONENTIAL FAMILY NONLINEAR MODELS

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Systems Science and Mathematical Sciences 1997年第3期10卷 193-201页

作者： zhu zhongyi WEI Bocheng(Department of Mathematics, Southeast University, Nanjing 210096, China)

In this paper, a necessary condition for the existence of any weakly consistentestimator is presented in exponential family nonlinear models. Then we give one morenecessary condition for a consistent estimator in generalized linear models. Under mildregularity conditions, the existence, the strong consistency and the asymptotic normalityof MLE are proved in exponential family nonlinear models. Our results may be regardedas a further work of [1] in generalized linear models.

关键词： Exponential family nonlinear models consistency asymptotic normality maximum likelihood estimator Fisher information matrix.

OFI-A COMPUTER-OPTICAL FABRIC ANALYSIS SYSTEM

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Scientia Geologica Sinica 1994年第3期 323-327页

作者： zhu zhongyi (China University of Geoscicnces, Wuhan 430074)

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Doubly Robust Estimation of Generalized Partial Linear Models for Longitudinal Data with Dropouts

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Doubly Robust Estimation of Generalized Partial Linear Model...