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Adaptive local linear Quantile regression

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Acta Mathematicae Applicatae Sinica 2011年第3期27卷 509-516页

作者： Yu-nan Su Mao-zai Tian Center for Applied Statistics School of Statistics Remin University of China Beijing 100872 China

In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation （MSE） and mean absolute estimation （MAE） criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.

关键词： quantile regression local linear regression adaptive smoothing automatic choice of window size Robustness

The M-estimate of local linear regression with Variable Window Breadth

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Northeastern Mathematical Journal 2005年第2期21卷 153-157页

作者：王新民董小刚蒋学军 School of Mathematics Jilin University 130012 Basic Science College Changchun University of Technology Changchun 130012 Department of Statistics Yunnan University Kunming 650091

In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.

关键词： local linear regression M-estimate nonparametric regression

Partially linear Single-Index Model in the Presence of Measurement Error

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Journal of Systems Science & Complexity 2022年第6期35卷 2361-2380页

作者： LIN Hongmei SHI Jianhong TONG Tiejun ZHANG Riquan School of Statistics and Information Shanghai University of International Business and EconomicsShanghai 201620China Key Laboratory of Advanced Theory and Application in Statistics and Data Science Ministry of EducationEast China Normal UniversityShanghai 200062China School of Mathematics and Computer Science Shanxi Normal UniversityLinfen 041081China Department of Mathematics Hong Kong Baptist UniversityHongKong 519087China School of Statistics East China Normal UniversityShanghai 200062China

The partially linear single-index model(PLSIM) is a flexible and powerful model for analyzing the relationship between the response and the multivariate covariates. This paper considers the PLSIM with measurement error possibly in all the variables. The authors propose a new efficient estimation procedure based on the local linear smoothing and the simulation-extrapolation method,and further establish the asymptotic normality of the proposed estimators for both the index parameter and nonparametric link function. The authors also carry out extensive Monte Carlo simulation studies to evaluate the finite sample performance of the new method, and apply it to analyze the osteoporosis prevention data.

关键词： local linear regression measurement error partially linear model SIMEX single-index model

TESTING SERIAL CORRELATION IN SEMIPARAMETRIC VARYING COEFFICIENT PARTIALLY linear ERRORS-IN-VARIABLES MODEL

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Journal of Systems Science & Complexity 2009年第3期22卷 483-494页

作者： Xuemei HU Feng LIU Zhizhong WANG Mathematics and Statistics College Chongqing Technology and Business University Chongqing 400067 China. School of Mathematics and Physics Chongqing InsLitu$e of Technology Chongqing 400050 China. School of Mathematics and Computing Technology Central South University Changsha 410075 China.

The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables *** test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial *** MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) *** results confirm that the proposed test performs satisfactorily in estimated sizeand power.

关键词： Asymptotic normality local linear regression measurement error modified profile leastsquares estimation partial linear model testing serial correlation varying coefficient model.

Approximating Conditional Density Functions Using Dimension Reduction

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Acta Mathematicae Applicatae Sinica 2009年第3期25卷 445-456页

作者： Jian-qing Fan Liang Peng Qi-wei Yao Wen-yang Zhang Department of Operations Research and Financial Engineering Princeton University Princeton NJ 08540 USA School of Mathematics Georgia Institute of Technology Atlanta GA 30332-0160 USA Department of Statistics London School of Economics London WC2A 2AE UK Department of Mathematical Sciences University of Bath Bath BA2 7AY UK

We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples.

关键词： Conditional density function dimension reduction, Kullback-Leibler discrepancy local linear regression nonparametric regression Shannon's entropy

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

Testing for Change Points in Partially linear Models

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Acta Mathematicae Applicatae Sinica 2015年第4期31卷 879-892页

作者： Li-wen ZHANG Zhong-yi ZHU School of Economics Shanghai University Department of Statistics School of ManagementFudan University

In this paper we provide a method to test the existence of the change points in the nonparametric regression function of partially linear models with conditional heteroscedastic variance. We propose the test statistic and establish its asymptotic properties under some regular conditions. Some simulation studies are given to investigate the performance of the proposed method in finite samples. Finally, the proposed method is applied to a real data for illustration.

关键词： change point partially linear model heteroscedastic variance local linear regression bandwidthselection