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Nonparametrie Quantile Inference for Cause-specific Residual Life Function Under Length-biased Sampling

Acta Mathematicae Applicatae Sinica 2020年第4期36卷 902-916页

作者： Fei-Peng ZHANG Cai-Yun FAN Yong ZHOU School of Economics and Finance Xi'an Jiaotong UniversityXi'an 710049China 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 MOE&Academy of Statistics and Interdisciplinary SciencesEast China Normal UniversityShanghai 200062China

This paper considers a competing risks model for right-censored and length-biased survival data from prevalent *** propose a nonparametric quantile inference procedure for cause-specific residual life distribution with competing risks *** also derive the asymptotic properties of the proposed estimators of this quantile *** studies and the unemployment data demonstrate the practical utility of the methodology.

关键词： Length-biased data competing risks quantile residual life estimating equation

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A class of admissible estimators of multiple regression coefficient with an unknown variance

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Statistical theory and Related Fields 2020年第2期4卷 190-201页

作者： Chengyuan Song Dongchu Sun Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghaiPeople’s Republic of China Department of Statistics University of Nebraska-LincolnLincolnNEUSA

Suppose that we observe y|θ,τ∼N_(p)(Xθ,τ^(−1)I_(p)),where θ is an unknown vector with unknown precisionτ.Estimating the regression coefficient θ with known τ has been well ***,statistical properties such as admissibility in estimating θ with unknownτare not well ***[(2009).Topics in shrinkage estimation and in causal inference(PhD thesis).Warton School,University of Pennsylvania]appears to be the first to consider the problem,developing sufficient conditions for the admissibility of estimating means of multivariate normal distributions with unknown *** generalise the sufficient conditions for admissibility and apply these results to the normal linear regression model.2-level and 3-level hierarchical models with unknown precisionτare investigated when a standard class of hierarchical priors leads to admissible estimators of θ under the normalised squared error *** reason to consider this problem is the importance of admissibility in the hierarchical prior selection,and we expect that our study could be helpful in providing some reference for choosing hierarchical priors.

关键词： Admissible estimators unknown variance multivariate normal distributions hierarchical models

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Proportional Mean Residual Life Model with Varying Coefficients for Length-Biased and Right-Censored data

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Acta Mathematica Sinica,English Series 2020年第5期36卷 578-596页

作者： Da XU Yong ZHOU Key Laboratory of Applied Statistics of MOE and School of Mathematics and Statistics Northeast Normal UniversityChangchun 130024P.R.China Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOEAcademy of Statistics and Interdisciplinary SciencesEast China Normal UniversityShanghai 200062P.R.China Academy of Mathematics and Systems Sciences Chinese Academy of SciencesBeijing 100190P.R.China

Length-biased data are encountered in many fields,including economics,engineering and epidemiological cohort *** are two main challenges in the analysis of such data:the assumption of independent censoring is violated and the assumed model for the underlying population is no longer satisfied for the observed *** this paper,a proportional mean residual life varyingcoefficient model for length-biased data is considered and a local pseudo likelihood method is proposed for estimating the coefficient functions in the *** properties are investigated for the proposed *** finite sample performance of the proposed methodology is demonstrated by simulation ***,the method is applied to a real data set concerning the Academy Awards.

关键词： Length-biased data proportional hazards model mean residual life varying-coefficient model

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The kth Power Expectile Estimation and Testing

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Communications in Mathematics and statistics 2024年第4期12卷 573-615页

作者： Fuming Lin Yingying Jiang Yong Zhou College of Mathematics and Statistics Sichuan University of Science and EngineeringZigongSichuanPeople’s Republic of China South Sichuan Center for Applied Mathematics ZigongSichuanPeople’s Republic of China Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOEand Academy of Statistics and Interdisciplinary Sciences and School of StatisticsEast China Normal UniversityShanghaiPeople’s Republic of China

This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression *** prove that the asymptotic covariance matrix of kth power expectile regression converges to that of quantile regression as k converges to one and hence promise a moment estimator of asymptotic matrix of quantile *** kth power expectile regression is then utilized to test for homoskedasticity and conditional symmetry of the *** comparisons of the local power among the kth power expectile regression tests,the quantile regression test,and the expectile regression test have been *** the underlying distribution is not standard normal,results show that the optimal k are often larger than 1 and smaller than 2,which suggests the general kth power expectile regression is ***,the methods are illustrated by a real example.

关键词： The kth power expectiles Expectiles Quantiles Testing for homoskedasticity Testing for conditional symmetry Estimating asymptotic matrix of quantile regression

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Exponential tilted likelihood for stationary time series models

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Statistical theory and Related Fields 2022年第3期6卷 254-263页

作者： Xiuzhen Zhang Yukun Liu Riquan Zhang Zhiping Lu Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOESchool of StatisticsEast China Normal UniversityShanghaiPeople’s Republic of China School of Mathematics and Statistics Shanxi Datong UniversityDatongPeople’s Republic of China

Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this *** to empirical likelihood(EL),it still suffers from two drawbacks:the nondefinition problem of the likelihood function and the under-coverage probability of confidence *** overcome these two problems,we further proposed the adjusted ET(AET)*** a specific adjustment level,our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET *** addition,due to the good performance of ET under moment model misspecification[Schennach,S.M.(2007).Point estimation with exponentially tilted empirical *** Annals of statistics,35(2),634–***://***/10.1214/009053606000001208],we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1).The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation.A real data set is analyzed for illustration purpose.

关键词： Exponential tilted likelihood adjusted exponential tilted likelihood stationary time series misspecified moment model

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Research on a quantification model of online learning cognitive load based on eye-tracking technology

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Multimedia Tools and applications 2024年 1-15页

作者： Xue, Yaofeng Zhu, Fangqing Li, Jiaxuan Department of Educational Information Technology and Shanghai Engineering Research Center of Digital Educational Equipment East China Normal University Shanghai200062 China Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal University Shanghai China

Online learning is characterized by a high degree of complexity and a wealth of information when compared to traditional classroom learning. This can have an adverse influence on the learning outcomes of online learners. The paper builds a quantification model of online learning cognitive load based on non-invasive eye-tracking technology by combining three eye-movement indicators: fixation time, fixation count, and pupil diameter. This is based on the analysis of cognitive load and eye-tracking technology. The study then uses a significant amount of eye movement experimental data in conjunction with the cognitive load test that students take in an online learning environment to confirm the viability and effectiveness of the quantification methodology. The paper builds a quantification model of online learning cognitive load based on non-invasive eye-tracking technology by combining three eye-movement indicators: fixation time, fixation count, and pupil diameter. This is based on the analysis of cognitive load and eye-tracking technology. The study then uses a significant amount of eye movement experimental data in conjunction with the cognitive load test that students take in an online learning environment to confirm the viability and effectiveness of the quantification methodology. © The Author(s), under exclusive licence to Springer science+Business Media, LLC, part of Springer Nature 2024.

关键词： Eye movements

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Semiparametric estimation for accelerated failure time mixture cure model allowing non-curable competing risk

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Statistical theory and Related Fields 2020年第1期4卷 97-108页

作者： Yijun Wang Jiajia Zhang Yincai Tang Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghai200062People’s Republic of China Department of Epidemiology and Biostatistics University of South CarolinaColumbiaSCUSA

The mixture cure model is the most popular model used to analyse the major event with a potential cure *** in the real world there may exist a potential risk from other non-curable competing *** this paper,we study the accelerated failure time model with mixture cure model via kernel-based nonparametric maximum likelihood estimation allowing non-curable competing *** EM algorithm is developed to calculate the estimates for both the regression parameters and the unknown error densities,in which a kernel-smoothed conditional profile likelihood is maximised in the M-step,and the resulting estimates are *** performance is demonstrated through comprehensive simulation ***,the proposed method is applied to the colorectal clinical trial data.

关键词： AFT mixture cure model competing risk EM algorithm

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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

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Novel View Synthesis on Unpaired data by Conditional Deformable Variational Auto-Encoder 1

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16th European Conference on Computer Vision, ECCV 2020

作者： Yin, Mingyu Sun, Li Li, Qingli Shanghai Key Laboratory of Multidimensional Information Processing East China Normal University Shanghai200241 China Key Laboratory of Advanced Theory and Application in Statistics and Data Science East China Normal University Shanghai200241 China

ISBN: (数字)9783030586041

ISBN: (纸本)9783030586034

Novel view synthesis often needs the paired data from both the source and target views. This paper proposes a view translation model under cVAE-GAN framework without requiring the paired data. We design a conditional deformable module (CDM) which uses the view condition vectors as the filters to convolve the feature maps of the main branch in VAE. It generates several pairs of displacement maps to deform the features, like the 2D optical flows. The results are fed into the deformed feature based normalization module (DFNM), which scales and offsets the main branch feature, given its deformed one as the input from the side branch. Taking the advantage of the CDM and DFNM, the encoder outputs a view-irrelevant posterior, while the decoder takes the code drawn from it to synthesize the reconstructed and the view-translated images. To further ensure the disentanglement between the views and other factors, we add adversarial training on the code. The results and ablation studies on MultiPIE and 3D chair datasets validate the effectiveness of the framework in cVAE and the designed module. © 2020, Springer Nature Switzerland AG.

关键词： Deformation

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Differentially Private Precision Matrix Estimation

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Acta Mathematica Sinica,English Series 2020年第10期36卷 1107-1124页

作者： Wen Qing SU Xiao GUO Hai ZHANG School of Mathematics Northwest UniversityXi'an 710127P.R.China Faculty of Information Technology Macao University of Science and TechnologyMacao 999078P.R.China Key Laboratory of Advanced Theory and Application in Statistics and Data Science(East China Normal University) Ministry of EducationShanghai 200062P.R.China

In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by using the alternating direction method of multipliers(ADMM) ***, we prove theoretical results showing that the differentially private ridge estimator for the precision matrix is consistent under fixed-dimension asymptotic, and establish a convergence rate of differentially private graphical lasso estimator in the Frobenius norm as both data dimension p and sample size n are allowed to grow. The empirical results that show the utility of the proposed methods are also provided.

关键词： Differential privacy graphical model ADMM algorithm

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