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Feature Screening for Ultrahigh-dimensional censored Data with Varying Coefficient Single-index Model

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Acta Mathematicae Applicatae Sinica 2019年第4期35卷 845-861页

作者： Yi LIU School of Mathematical Sciences Ocean University of China

In this paper, we study the sure independence screening of ultrahigh-dimensional censored data with varying coefficient single-index model. This general model framework covers a large number of commonly used survival models. The property that the proposed method is not derived for a specific model is appealing in ultrahigh dimensional regressions, as it is difficult to specify a correct model for ultrahigh dimensional *** the assuming data generating process does not meet the actual one, the screening method based on the model will be problematic. We establish the sure screening property and consistency in ranking property of the proposed method. Simulations are conducted to study the finite sample performances, and the results demonstrate that the proposed method is competitive compared with the existing methods. We also illustrate the results via the analysis of data from The National Alzheimers Coordinating Center(NACC).

关键词： censored data consistency in ranking property feature selection high-dimensional data sure screening property varying coefficient single-index model

Hypothesis Testing with Paired Partly Interval censored Data

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 541-548页

作者： Ding-jiao CAI Bo LU Xing-wei TONG School of Mathematics and Information Science Henan University of Economics and LawZhengzhou 450046China Division of Biostatistics College of Public HealthOhio State UniversityColumbusOhio43210U.S.A School of Statistics Beijing Normal UniversityBeijing 100875China

Partly interval censored data frequently occur in many areas including clinical trials,epidemiology research,and medical follow-up *** data come from observational studies,we need to carefully adjust for the confounding bias in order to estimate the true treatment *** matching designs are popular for removing confounding bias without parametric *** time-to-event outcomes,there are some literature for hypothesis testing with paired right censored data,but not for interval censored data.O’Brien and Fleming extended the Prentice Wilcoxon test to right censored paired data by making use of the PrenticeWilcoxon *** proposed the Akritas test and established its asymptotic *** extend Akritas test to partly interval censored *** estimate the survival distribution function by nonparametric maximum likelihood estimation(NPMLE),and prove the asymptotic validity of the new *** improve our test under small sample size or extreme distributions,we also propose a modified version using the rank of the score *** results indicate that our proposed methods have very good performance.

关键词： partly interval censored data nonparametric maximum likelihood estimation Wilcoxon signed rank test

LAD estimation for nonlinear regression models with randomly censored data

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Science China Mathematics 2005年第7期48卷 880-897页

作者： ZHOU Xiuqing WANG Jinde School of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 China Department of Mathematics Nanjing University Nanjing 210093 China Department of Mathematics Nanjing University Nanjing 210093 China

The least absolute deviations (LAD) estimation for nonlinear regression models with randomly censored data is studied and the asymptotic properties of LAD estimators such as consistency, boundedness in probability and asymptotic normality are established. Simulation results show that for the problems with censored data, LAD estimation performs much more robustly than the least squares estimation.

关键词： randomly censored data, nonlinear regression model, LAD estimator, asymptotic normality.

Edgeworth expansion of the Studentized product-limit estimator for truncated and censored data

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Science China Mathematics 2000年第5期43卷 495-508页

作者：孙六全 Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribut... 详细信息

关键词： truncated and censored data Studentized product-limit estimator asymptotic normality Edge- worth expansion.

Distribution Approximation of Shrinkage Estimate in censored Regression Model via Randomly Weighting Method

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Acta Mathematicae Applicatae Sinica 2019年第2期35卷 421-434页

作者： Xian-hui LIU Zhan-feng WANG Yao-hua WU Department of Statistics and Finance University of Science and Technology of China School of Statistics and Research Center of Applied Statistics Jiangxi University of Finance and Economics

censored regression("Tobit") model is a special case of limited dependent variable regression model, and plays an important role in econometrics. Based on this model, all kinds of methods for variable or group variable selection have been developed and the corresponding shrinkage parameter estimates are widely studied. However, asymptotic distributions of the shrinkage estimates involve unknown nuisance parameters,such as density function of error term. To avoid estimating nuisance parameters, this paper presents a randomly weighting method to approximate to the asymptotic distribution of the shrinkage estimate. A computation procedure of random approximation is provided and asymptotic properties of the randomly weighting estimates are also obtained. The proposed methods are evaluated with extensively numerical studies and a women labor supply example.

关键词： censored regression model variable selection asymptotic properties randomly weighting

Asymptotic theory of nonparametric regression estimates with censored data

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Science China Mathematics 2000年第6期43卷 574-580页

作者：施沛德王海燕张利华 Department of Probability and Statistics Peking University Beijing 100871china

For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literature, but the optimal rates of global convergence have not been obtained yet. Because of the possible information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression function based on right-censored response data, and proves, under some regularity conditions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtain the asymptotic optimality of AIC, AICC, GCV, CP, and FPE criteria in the process of selecting the parameters.

关键词： nonparametric regression censored data regression spline optimal rates of convergence.

Bayesian empirical likelihood and variable selection for censored linear model with applications to acute myelogenous leukemia data

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International Journal of Biomathematics 2019年第5期12卷 43-61页

作者： Chun-Jing Li Hong-Mei Zhao Xiao-Gang Dong School of Mathematics Jilin University Jilin Changchun 130012P.R.China School of Mathematics and Statistics Changchun University of Technology Jilin Changchun 130012 P.R.China

This paper develops the Bayesian empirical likelihood (BEL) method and the BEL vari-able selection for linear regression models with censored *** likelihood is a multivariate analysis tool that has been widely applietl to many fieltls such as biomed-ical and social *** introducing two special priors to the empirical likelihood function,we find two obvious superiorities of the BEL methods,that is (i) more precise coverage probabilities of the BEL credible region and (ii) higher accuracy and correct identification rate of the BEL model selection using an hierarchical Bayesian models *** current methods such as the LASSO,A LASSO and *** numerical simu-lations and empirical analysis of two data examples show strong competitiveness of the proposed method.

关键词： Bayesian empirical likeliliood censored linear regression coverage probabili-ties spike-and-slab prior

THE RATE OF UNIFORM CONVERGENCE OF THE SURVIVAL FUNCTION ESTIMATOR FOR TRUNCATED AND censored DATA

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Journal of Systems Science & Complexity 2001年第1期14卷 93-105页

作者： SUN Liuquan (Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China) 中科院应用数学所北京 100080

For left truncated and right censored data, based on a strong representation of the product-limit estimator of the survival function, we derive the sufficient and necessary condition for the rate of strong uniform con... 详细信息

关键词： Truncated and censored data product-limit estimator strong representation rate of uniform convergence.

LOCAL ASYMPTOTIC PROPERTIES OF HAZARD RATE ESTIMATORS FOR TRUNCATED AND censored DATA

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Journal of Systems Science & Complexity 2001年第4期14卷 413-424页

作者： SUN Liuquan, WU Guofu, WEI Xianhua (Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China) 中科院应用数学所北京 100080

Functional laws of the iterated logarithm are obtained for cumulative hazard processes in the neighborhood of a fixed point when the data are subject to left truncation and right censorship. On the basis of these results the exact rates of pointwise almost sure convergence for various types of kernel hazard rate estimators are derived.

关键词： Truncated and censored data hazard rate kernel estimation nearest neighbor estimation law of the iterated logarithm.