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Two-Stage Online Debiased Lasso Estimation and Inference for High-Dimensional Quantile Regression with Streaming Data

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Journal of Systems Science & Complexity 2024年第3期37卷 1251-1270页

作者： PENG Yanjin WANG Lei School of Statistics and Data Science KLMDASRLEBPS and LPMCNankai UniversityTianjin 300071China

In this paper,the authors propose a two-stage online debiased lasso estimation and statistical inference method for high-dimensional quantile regression(QR)models in the presence of streaming data.In the first stage,the authors modify the QR score function based on kernel smoothing and obtain the online lasso smoothed QR estimator through iterative algorithms.The estimation process only involves the current data batch and specific historical summary statistics,which perfectly accommodates to the special structure of streaming data.In the second stage,an online debiasing procedure is carried out to eliminate biases caused by the lasso penalty as well as the accumulative approximation error so that the asymptotic normality of the resulting estimator can be established.The authors conduct extensive numerical experiments to evaluate the performance of the proposed method.These experiments demonstrate the effectiveness of the proposed method and support the theoretical results.An application to the Beijing PM2.5 Dataset is also presented.

关键词： Adaptive tuning asymptotic normality debiased lasso online updating quantile regres-sion

asymptotic normality OF PARAMETERSESTIMATION IN EV MODEL WITH REPLICATEDOBSERVATIONS

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Acta Mathematica Scientia 2002年第1期22卷 107-114页

作者：张三国陈希孺 Graduate School of the University of Science and Technology of China Graduate School of the Chinese Academy of Sciences Beijing 100039 China

This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptot... 详细信息

关键词： errors-in-variables model asymptotic normality replicated observations

asymptotic normality OF THE NEAREST NEIGHBOR HAZARD ESTIMATES

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Acta Mathematicae Applicatae Sinica 2000年第2期16卷 188-198页

作者：卢江顾鸣高冯琦琳 University of the Witwatersrand Wits South Africa McGill University Montréal Canada Beijing College of Adult Education Beijing China

The nearest neighbor (n.n.) and its related methods are widely used in density and hazard function estimations. Even though the asymptotic normality of the n.n. density estimate is well known (see [1]), similar results for the n.n. hazard estimate have not been shown in the literature. In this paper, we develop a different approach to deal with the n.n. type estimator. For a mixed censorship-truneation model, we show that, under mild conditions, the n. n. estimate can be approximated by an estimate formed with a proper fixed bandwidth sequence and derive the asymptotic normality as a consequence.

关键词： asymptotic normality censorship- truncation model , density function hazard function, kernel estimator nearest neighbor estimate

THE CONSISTENCY AND asymptotic normality OF NEAREST NEIGHBOR DENSITY ESTIMATOR UNDER α-MIXING CONDITION

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Acta Mathematica Scientia 2010年第3期30卷 733-738页

作者：刘妍岩张艳丽 School of Mathematics and Statistics Wuhan University Institute of Statistics and Actuary Shandong Economic University

We investigate the consistency and asymptotic normality of nearest-neighbor density estimator of a sample data process based on α-mixing assumption. We extend the correspondent result under independent identical cases.

关键词： NN-estimator a-mixing consistency asymptotic normality

Consistency and asymptotic normality of the Maximum Quasi-likelihood Estimator in Quasi-likelihood Nonlinear Models with Random Regressors

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Acta Mathematicae Applicatae Sinica 2010年第2期26卷 241-250页

作者： Tian Xia Shun-fang Wang Xue-ren Wang Department of Statistics Yunnan University Kunming 650091 China School of Information Science and Engineering Yunnan University Kunming 650091 China

This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.

关键词： asymptotic normality consistency maximum quasi-likelihood estimator quasi-likelihood nonlinear models with random regressors

Consistency and asymptotic normality of MLE of Parameter Vector in a Randomly Censored GLM with Incomplete Information

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Wuhan University Journal of Natural Sciences 2006年第2期11卷 333-338页

作者： XIAO Zhihong LIU Luqin School of Mathematics and Statistics Wuhan University Wuhan 430072 Hubei China School of Sciences Huazhong Agricultural University Wuhan 430070 Hubei China

The generalized linear model（GLM） based on the observed data with incomplete information in the case of random censorship is defined. Under the given conditions, the existence and uniqueness of the solution on the likelihood equations with respect to the parameter vector β of the model are discussed, and the consistency and asymptotic normality of the maximum likelihood estimator（MLE） βn^-, are proved.

关键词： GLM incomplete information MLE consistency asymptotic normality

asymptotic normality OF THE NONPARAMETRIC KERNEL ESTIMATION OF THE CONDITIONAL HAZARD FUNCTION FOR LEFT-TRUNCATED AND DEPENDENT DATA

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Annals of Applied Mathematics 2018年第4期34卷 395-406页

作者： Meijuan Ou Xianzhu Xiong Yi Wang College of Math and Computer ScienceFuzhou UniversityFuzhou 350116FujianPR China

Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed ... 详细信息

关键词： asymptotic normality Nadaraya-Watson estimation local linear estimation conditional hazard function left-truncated data

asymptotic normality of Multi-Dimension Quasi Maximum Likelihood Estimate in Generalized Linear Models withAdaptive Design

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Wuhan University Journal of Natural Sciences 2006年第2期11卷 328-332页

作者： LI Guoliang GAO Qibing LIU Luqin School of Mathematics and Statistics Wuhan University Wuhan 430072 Hubei China Department of Statistics and Finance University of Science and Technology of China Hefei 230026 Anhui China

We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is... 详细信息

关键词： generalized linear model（GLM） adaptive desigm the quasi likelihood estimate asymptotic normality

A New Location Invariant Moment-Type Estimator and Its asymptotic normality

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Journal of Mathematical Research with Applications 2018年第3期38卷 293-302页

作者： Weiqi LIU Shanshan LIANG Research Center for Management and Decision Making Shanxi University Faculty of Finance and Banking Shanxi University of Finance and Economics School of Mathematical Sciences Shanxi University

The moment estimator has been widely used in extreme value theory in order to estimate the extreme value index, however it is not location invariant. In this paper, based on the moment-type estimator, we propose a new location invariant moment-type estimator,and discuss its asymptotic normality under the second order regular variation. Finally, a simulation is presented to compare this new estimator with another location invariant momenttype estimator γ;（k;, k） proposed by Ling, which indicates that the new estimator has good performances.

关键词： extreme value index moment-type estimator regular variation location invariant asymptotic normality