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inference for longitudinal data from complex sampling surveys: An approach based on quadratic inference functions

SCANDINAVIAN JOURNAL OF STATISTICS 2021年第1期48卷 246-274页

作者： Dumitrescu, Laura Qian, Wei Rao, J. N. K. Victoria Univ Wellington Sch Math & Stat Wellington New Zealand Stat Canada Ottawa ON Canada Carleton Univ Sch Math & Stat Ottawa ON Canada

We propose a survey weighted quadratic inference function method for the analysis of data collected from longitudinal surveys, as an alternative to the survey weighted generalized estimating equation method. The procedure yields estimators of model parameters, which are shown to be consistent and have a limiting normal distribution. Furthermore, based on the inference function, a pseudolikelihood ratio type statistic for testing a composite hypothesis on model parameters and a statistic for testing the goodness of fit of the assumed model are proposed. We establish their asymptotic distributions as weighted sums of independent chi-squared random variables and obtain Rao-Scott corrections to those statistics leading to a chi-squared distribution, approximately. We examine the performance of the proposed methods in a simulation study.

关键词： asymptotic normality complex sampling design consistency goodness of fit quadratic inference functions super-population model

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Quantile regression for panel count data based on quadratic inference functions

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JOURNAL OF STATISTICAL PLANNING AND inference 2020年第0期207卷 230-245页

作者： Wang, Weiwei Wu, Xianyi Zhao, Xiaobing Zhou, Xian Zhejiang Gongshang Univ Sch Stat & Math Hangzhou Zhejiang Peoples R China East China Normal Univ Sch Stat Shanghai Peoples R China Zhejiang Univ Finance & Econ Sch Data Sci Hangzhou Zhejiang Peoples R China Macquarie Univ Dept Actuarial Studies & Data Analyt N Ryde NSW Australia

Panel count data frequently arise in such areas as medical research and reliability studies, and various estimation methods have been developed for analyzing this type of data. In the literature, however, there are few methods incorporating the correlation within subjects. In this paper, on the basis of quadratic inference functions, we apply the quantile regression to analyze panel count data with time-varying coefficients. The proposed procedure can easily take into account the correlation within subjects and yields more efficient estimators even if the working correlation is misspecified. An efficient nonparametric hypothesis test is also proposed to determine whether coefficient functions are time varying or time invariant. Asymptotic results for the proposed estimators are established under some regularity conditions. Simulation studies are carried out to evaluate the finite-sample behavior of the method and to compare the estimation efficiency. Finally, an application of the method is demonstrated by re-analyzing a dataset from a bladder tumor study. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Panel count data Time-varying coefficient Quantile regression quadratic inference functions Spline functions

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Efficient parameter estimation for multivariate accelerated failure time model via the quadratic inference functions method

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RANDOM MATRICES-THEORY AND APPLICATIONS 2019年第4期8卷

作者： Fu, Liya Yang, Zhuoran Zhao, Mingtao Zhou, Yan Xi An Jiao Tong Univ Sch Math & Stat Xian Shaanxi Peoples R China Shenzhen Univ Inst Stat Sci Coll Math & Stat Shenzhen Peoples R China Anhui Univ Finance & Econ Inst Stat & Appl Math Bengbu Anhui Peoples R China

A popular approach, generalized estimating equations (GEE), has been applied to the multivariate accelerated failure time (AFT) model of the clustered and censored data. However, this method needs to estimate the correlation parameters and calculate the inverse of the correlation matrix. Meanwhile, the efficiency of the parameter estimators is low when the correlation structure is misspecified and/or the marginal distribution is heavy-tailed. This paper proposes using the quadratic inference functions (QIF) with a mixture correlation structure to estimate the coefficients in the multivariate AFT model, which can avoid estimating the correlation parameters and computing the inverse matrix of the correlation matrix. Moreover, the estimator derived from the QIF is consistent and asymptotically normal. Simulation studies indicate that the proposed method outperforms the method based on GEE when the marginal distribution has a heavy tail. Finally, the proposed method is used to analyze a real dataset for illustration.

关键词： quadratic inference functions generalized estimating equations within-cluster correlation

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Penalized quadratic inference functions for semiparametric varying coefficient partially linear models with longitudinal data

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JOURNAL OF MULTIVARIATE ANALYSIS 2014年第0期132卷 94-110页

作者： Tian, Ruiqin Xue, Liugen Liu, Chunling Beijing Univ Technol Coll Appl Sci Beijing 100124 Peoples R China Hong Kong Polytech Univ Dept Appl Math Hong Kong Hong Kong Peoples R China

In this paper, we focus on the variable selection for semiparametric varying coefficient partially linear models with longitudinal data. A new variable selection procedure is proposed based on the combination of the basis function approximations and quadratic inference functions. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency and asymptotic normality of the resulting estimators. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure. We further illustrate the proposed procedure by an application. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Semiparametric varying coefficient partially linear models Variable selection Longitudinal data quadratic inference functions

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Estimation and variable selection of quantile partially linear additive models for correlated data

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2024年第2期94卷 315-345页

作者： Zhao, Weihua Li, Rui Lian, Heng Nantong Univ Sch Sci Nantong Peoples R China Shanghai Univ Int Business & Econ Sch Stat & Informat Shanghai Peoples R China City Univ Hong Kong Dept Math Hong Kong Peoples R China

Longitudinal data arise frequently in many economic studies and epidemiological research. In this paper, we investigate the partially linear additive model for longitudinal data in the framework of quantile regression. To incorporate the within-subject correlation, we develop an estimation procedure using quadratic inference function (QIF) and polynomial spline approximation for unknown nonparametric functions. The theoretical properties of the resulting estimators are established, where the nonparametric functions achieve the optimal convergence rate and the parametric components are asymptotically normal even when the number of parameters in the linear part is diverging. We also propose a variable selection procedure based on penalization. Since the objective function is discontinuous, a practical estimation procedure is proposed using induced smoothing and we prove that the smoothed estimator is asymptotically equivalent to the original estimator. The proposed methods are evaluated via simulation studies and a real data application.

关键词： Longitudinal data partially linear additive models quadratic inference functions quantile regression

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STATISTICS & PROBABILITY LETTERS 2024年 211卷

作者： Geng, Shuli Zhang, Lixin Zhejiang Univ Sch Math Sci Hangzhou 31000 ZJ Peoples R China

This paper focuses on decorrelated empirical likelihood -based inference for longitudinal data with ultrahigh -dimensional covariates. The primary issues we aim to address involve parameter estimation and hypothesis testing for a low -dimensional parameter of interest. Under the framework of the generalized linear model, we initially consider the within -subject correlation by linearizing the precision matrix with certain known matrices, which retains optimality even if the working correlated structure is misspecified. Coupled with the decorrelated matrix, we then eliminate the influence of nuisance parameters on the estimation procedure. The proposed approach not only yields more efficient estimators compared to generalized decorrelated estimating equations but also shares the same asymptotic variance as quadratic decorrelated inference function based methods. Furthermore, we define the decorrelated empirical loglikelihood ratio test statistic to assess the significance of regression coefficients. Finally, to evaluate the performance of the proposed procedure, we conduct simulation studies and apply it to a real data example.

关键词： Generalized linear models Empirical likelihood Decorrelated matrix quadratic inference functions High-dimensional longitudinal data

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Estimation in quantile regression models for correlated data with diverging number of covariates and large cluster sizes

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2023年第4期52卷 1012-1038页

作者： Zhao, Weihua Zhang, Xiaoyu Yuen, Kam Chuen Li, Rui Lian, Heng Nantong Univ Sch Sci Nantong Peoples R China Univ Hong Kong Dept Stat Pok Fu Lam Hong Kong Peoples R China Shanghai Univ Int Business & Econ Sch Stat & Informat Shanghai 201620 Peoples R China City Univ Hong Kong Dept Math Kowloon Tong Hong Kong Peoples R China

In many data analytic problems, repeated measurements with a large number of covariates are collected and conditional quantile modeling for such correlated data are often of significant interest, especially in medical applications. We propose a quadratic inference functions based approach to take into account the correlations within clusters and use smoothing to make the objective function amenable to computation. We show that the asymptotic properties of the estimators are the same whether or not smoothing is applied, established in the "diverging p, large n" setting. The cluster sizes are also allowed to diverge with sample size n. Simulation results are presented to demonstrate the effectiveness of the proposed estimator by taking into account the within-cluster correlations and we use a longitudinal data set to illustrate the method.

关键词： Clustered data diverging dimensionality induced smoothing quadratic inference functions quantile regression

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Robust empirical likelihood inference for partially linear varying coefficient models with longitudinal data

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2023年第10期93卷 1559-1579页

作者： Sun, Huihui Liu, Qiang Capital Univ Econ & Business Sch Stat Beijing Peoples R China Yancheng Teachers Univ Sch Math & Stat Yancheng Peoples R China Capital Univ Econ & Business Sch Stat Beijing 100070 Peoples R China

This paper presents a robust empirical likelihood procedure based on the exponential squared loss (ESL) function and leverage-based weights for the partially linear varying coefficient model with longitudinal data. The proposed method simultaneously solves the problems of correlation structure of longitudinal data and the existence of outliers, and achieves robustness and efficiency by introducing an appropriate data-driven tuning parameter. More importantly, profit from the QR decomposition technique, our method allows the parametric and nonparametric parts of the models to be estimated separately, which can avoid the mutual influence between them and make the implementation easier. Under some mild conditions, the large sample theoretical properties of the robust empirical likelihood approach are established. Simulation studies and a real data analysis are also carried out to assess and illustrate the finite sample performance.

关键词： Longitudinal partially linear varying coefficient models exponential squared loss robust empirical likelihood QR decomposition quadratic inference functions

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Smooth-Threshold GEE Variable Selection Based on quadratic inference functions with Longitudinal Data

Smooth-Threshold GEE Variable Selection Based on Quadratic I...

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4th International Conference on Information Computing and Applications (ICICA)

作者： Tian, Ruiqin Xue, Liugen Beijing Univ Technol Coll Appl Sci Beijing 100124 Peoples R China

ISBN: (纸本)9783642539329;9783642539312

A variable selection procedure is proposed using smooth-threshold generalized estimating equations based on quadratic inference functions (SGEE-QIF). The proposed procedure automatically eliminates inactive predictors by setting the corresponding parameters to be zero, and simultaneously estimates the nonzero regression coefficients by solving the SGEE-QIF. The proposed procedure avoids the convex optimization problem and is flexible and easy to implement. We establish the consistency and asymptotic normality of the resulting estimators. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure.

关键词： quadratic inference functions Variable selection Longitudinal data Generalized estimating equations

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A methodology for improving efficiency estimation based on conditional mix-GEE models in longitudinal studies

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2022年第1期51卷 254-265页

作者： Xing, Yanchun Ma, Wenqing Liang, Chunhui Jilin Univ Finance & Econ Sch Stat Changchun Jilin Peoples R China Northeast Normal Univ Sch Math & Stat Changchun 130024 Jilin Peoples R China

Estimating random effects accurately is crucial since it reflects the subject-specific effect in longitudinal studies. In this paper, we develop a new methodology for improving the efficiency of fixed-effects and random-effects estimation based on conditional mix-GEE models. The advantage of our proposed approach is that the serial correlation over time was accommodated in estimating random effects. Meanwhile, the normality assumption for random effects is not required. In addition, according to the estimates of some mixture proportions, the true working correlation matrix can be identified. The feature of our proposed approach is that the estimators of the regression parameters are more efficient than CCQIF, cmix-GEE and CQIF approaches even if the working correlation structure is not correctly specified. In theory, we show that the proposed method yields a consistent and more efficient estimator than the random-effect estimator that ignores correlation information from longitudinal data. We establish asymptotic results for both fixed-effects and random-effects estimators. Simulation studies confirm the performance of our proposed method.

关键词： Conditional mix-GEE Random effects quadratic inference functions Longitudinal data

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