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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

A short note on fitting a single-index model with massive data

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Statistical Theory and Related Fields 2023年第1期7卷 49-60页

作者： Rong Jiang Yexun Peng Department of Statistics College of ScienceDonghua UniversityShanghaiPeople’s Republic of China

This paper studies the inference problem of index coefficient in single-index models under massive *** of massive dataset is challenging owing to formidable computational costs or memory requirements.A natural method is the averaging divide-and-conquer approach,which splits data into several blocks,obtains the estimators for each block and then aggregates the estimators via ***,there is a restriction on the number of *** overcome this limitation,this paper proposed a computationally efficient method,which only requires an initial estimator and then successively refines the estimator via multiple rounds of *** proposed estimator achieves the optimal convergence rate without any restriction on the number of *** present both theoretical analysis and experiments to explore the property of the proposed method.

关键词： single-index model massive dataset divide-and-conquer method

Empirical likelihood for single-index models with responses missing at random

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Science China Mathematics 2016年第6期59卷 1187-1207页

作者： XUE LiuGen LIAN Heng College of Applied Sciences Beijing University of Technology School of Mathematics and Statistics University of New South Wales

The missing response problem in single-index models is studied, and a bias-correction method to infer the index coefficients is developed. Two weighted empirical log-likelihood ratios with asymptotic chisquare are derived, and the corresponding empirical likelihood confidence regions for the index coefficients are constructed. In addition, the estimators of the index coefficients and the link function are defined, and their asymptotic normalities are proved. A simulation study is conducted to compare the empirical likelihood and the normal approximation based method in terms of coverage probabilities and average lengths of confidence intervals. A real example illustrates our methods.

关键词： single-index model empirical likelihood confidence region index coefficient missing response

single-index Quantile Regression with Left Truncated Data

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Journal of Systems Science & Complexity 2022年第5期35卷 1963-1987页

作者： XU Hongxia FAN Guoliang LI Jinchang Department of Mathematics Shanghai Maritime UniversityShanghai 201306China School of Data Sciences Zhejiang University of Finance and EconomicsHangzhou 310018China School of Economics and Management Shanghai Maritime UniversityShanghai 201306China

The purpose of this paper is two ***,the authors investigate quantile regression(QR)estimation for single-index QR models when the response is subject to random left *** random weights are introduced to deal with left truncated data and the associated iteration estimation method is *** asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both ***,by combining the QR loss function and the adaptive LASSO penalization,a variable selection procedure for the index parameter is introduced and its oracle property is ***,a weighted empirical log-likelihood ratio of the index parameter based on the QR method is introduced and is proved to be asymptotic standard chi-square ***,confidence regions of the index parameter can be *** finite sample performance of the proposed methods are demonstrated.A real data analysis is also conducted to show the usefulness of the proposed approaches.

关键词： Adaptive LASSO penalty left truncated data quantile regression single-index model variable selection