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学者姓名：张忠占
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摘要 ：
A new metric, called variation of conditional mean (VCM), is proposed to measure the dependence of conditional mean of a response variable on a predictor variable. The VCM has several appealing merits. It equals zero if and only if the conditional mean of the response is independent of the predictor; it can be used for both real vector-valued variables and functional data. An estimator of the VCM is given through kernel smoothing, and a test for the conditional mean independence based on the estimated VCM is constructed. The limit distributions of the test statistic under the null hypothesis and alternative hypothesis are deduced, respectively. We further use VCM as a marginal utility to do high-dimensional feature screening to screen out variables that do not contribute to the conditional mean of the response given the predictors and prove the validity of the sure screening property. Furthermore, we find the cross variation of conditional mean (CVCM), a variant of the VCM, has a faster convergence rate than the VCM under conditional mean independence. Numerical comparison shows that the VCM and CVCM performs well in both conditional independence testing and feature screening. We also illustrate their applications to real data sets.
关键词 ：
functional data functional data feature screening feature screening kernel regression kernel regression conditional mean dependence conditional mean dependence
引用：
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| GB/T 7714 | Tian, Zhentao , Lai, Tingyu , Zhang, Zhongzhan . Variation of conditional mean and its application in ultrahigh dimensional feature screening [J]. | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2024 , 54 (2) : 352-382 . |
| MLA | Tian, Zhentao 等. "Variation of conditional mean and its application in ultrahigh dimensional feature screening" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 54 . 2 (2024) : 352-382 . |
| APA | Tian, Zhentao , Lai, Tingyu , Zhang, Zhongzhan . Variation of conditional mean and its application in ultrahigh dimensional feature screening . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2024 , 54 (2) , 352-382 . |
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摘要 ：
This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model. A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model. The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis, and tends to infinity in probability under the alternative hypothesis, which implies the consistency of the test. Furthermore, it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis. Extensive simulations are reported, and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies. The proposed methods are also applied to two real datasets.
关键词 ：
consistent test consistent test Composite quantile regression Composite quantile regression quadratic form quadratic form nonparametric test nonparametric test functional data functional data
引用：
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| GB/T 7714 | Xia, Lili , Du, Jiang , Zhang, Zhongzhan . A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models [J]. | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY , 2024 , 37 (4) : 1714-1737 . |
| MLA | Xia, Lili 等. "A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models" . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 37 . 4 (2024) : 1714-1737 . |
| APA | Xia, Lili , Du, Jiang , Zhang, Zhongzhan . A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY , 2024 , 37 (4) , 1714-1737 . |
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摘要 ：
We propose a new test for the specification of linear spatial autoregressive models where the spatial weights matrix is pre specified. Our test is built on the difference of two estimates of the spatial parameter where the two estimates are obtained by the parametric and nonparametric GMM estimation methods, respectively. Under mild assumptions, we derive the limiting null distribution and show consistency for our test. Unlike the general nonparametric test, our test can detect the local alternatives that approach the null at a rate n-1/2, where n is the sample size. Monte Carlo simulations are conducted to study the finite sample performance of our test. Finally, we apply our test to check the model specification for the economic growth rate example.(c) 2023 Elsevier B.V. All rights reserved.
关键词 ：
GMM estimation GMM estimation Spatial parameter Spatial parameter Consistent test Consistent test Nonparametric models Nonparametric models Spatial autoregression Spatial autoregression
引用：
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| GB/T 7714 | Tang, Yangbing , Du, Jiang , Zhang, Zhongzhan . A parametric specification test for linear spatial autoregressive models [J]. | SPATIAL STATISTICS , 2023 , 57 . |
| MLA | Tang, Yangbing 等. "A parametric specification test for linear spatial autoregressive models" . | SPATIAL STATISTICS 57 (2023) . |
| APA | Tang, Yangbing , Du, Jiang , Zhang, Zhongzhan . A parametric specification test for linear spatial autoregressive models . | SPATIAL STATISTICS , 2023 , 57 . |
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摘要 ：
The estimation of the average treatment effect on the treated (ATT) plays an essential role when the effect of an intervention or a treatment on those participants who actually received it is the focus. However, the validity of conventional estimation methods relies on the precise measurement of variables. Misclassified category outcome variables may cause non-negligible bias when estimating ATT. In this paper, under the assumption that the misclassification probability is homogeneous, we develop a bias-corrected estimation method to consistently estimate ATT when internal validation data are available for a subgroup of the study population. We further derive a doubly robust estimator by augmenting the bias-corrected estimator to provide protection against treatment model misspecification. Through simulation experiments and real data analysis, we demonstrate the satisfactory performance of the proposed estimators.
关键词 ：
average treatment effect on the treated average treatment effect on the treated inverse probability weighting inverse probability weighting misclassification misclassification causal inference causal inference double robustness double robustness
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| GB/T 7714 | Wei, Shaojie , Zhang, Zhongzhan , Li, Gaorong . Estimation of the average treatment effect on the treated with misclassified binary outcome [J]. | STAT , 2022 , 11 (1) . |
| MLA | Wei, Shaojie 等. "Estimation of the average treatment effect on the treated with misclassified binary outcome" . | STAT 11 . 1 (2022) . |
| APA | Wei, Shaojie , Zhang, Zhongzhan , Li, Gaorong . Estimation of the average treatment effect on the treated with misclassified binary outcome . | STAT , 2022 , 11 (1) . |
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摘要 ：
响应变量删失时函数型部分线性分位数回归模型的估计
关键词 ：
自助法 自助法 函数型主成分分析 函数型主成分分析 分位数回归 分位数回归 随机删失 随机删失 函数型预测量 函数型预测量
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| GB/T 7714 | 史功明 , 张忠占 , 谢田法 et al. 响应变量删失时函数型部分线性分位数回归模型的估计 [J]. | 史功明 , 2021 , 51 (3) : 152-166 . |
| MLA | 史功明 et al. "响应变量删失时函数型部分线性分位数回归模型的估计" . | 史功明 51 . 3 (2021) : 152-166 . |
| APA | 史功明 , 张忠占 , 谢田法 , 数学的实践与认识 . 响应变量删失时函数型部分线性分位数回归模型的估计 . | 史功明 , 2021 , 51 (3) , 152-166 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
最近几年,函数型数据分析的理论和应用飞速发展.在许多实际应用里,响应变量往往存在随机右删失的情况.考虑利用函数型部分线性分位数回归模型来刻画函数型和标量预测量与右删失响应变量之间的关系.基于函数型主成分基函数来逼近未知的斜率函数,通过极小化逆概率加权分位数损失函数得到未知系数的估计量.文章的估计方法容易通过加权分位数回归程序实现.在一定的假设条件下,给出了有限维参数估计量的渐近正态性与斜率函数估计量的收敛速度.最后,通过模拟计算与应用实例证明了所提方法的有效性.
关键词 ：
分位数回归 分位数回归 随机删失 随机删失 函数型主成分分析 函数型主成分分析 函数型预测量 函数型预测量 自助法 自助法
引用：
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| GB/T 7714 | 史功明 , 张忠占 , 谢田法 . 响应变量删失时函数型部分线性分位数回归模型的估计 [J]. | 数学的实践与认识 , 2021 , 51 (3) : 152-166 . |
| MLA | 史功明 et al. "响应变量删失时函数型部分线性分位数回归模型的估计" . | 数学的实践与认识 51 . 3 (2021) : 152-166 . |
| APA | 史功明 , 张忠占 , 谢田法 . 响应变量删失时函数型部分线性分位数回归模型的估计 . | 数学的实践与认识 , 2021 , 51 (3) , 152-166 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
We propose a new nonparametric independence test for two functional random variables. The test is based on a new dependence metric, the so-called angle covariance, which fully characterizes the independence of the random variables and generalizes the projection covariance proposed for random vectors. The angle covariance has a number of desirable properties, including the equivalence of its zero value and the independence of the two functional variables, and it can be applied to any functional data without finite moment conditions. We construct a V-statistic estimator of the angle covariance, and show that it has a Gaussian chaos limiting distribution under the independence null hypothesis and a normal limiting distribution under the alternative hypothesis. The test based on the estimated angle covariance is consistent against all alternatives and easy to be implemented by the given random permutation method. Simulations show that the test based on the angle covariance outperforms other competing tests for functional data. (C) 2020 Elsevier Inc. All rights reserved.
关键词 ：
Angle covariance Angle covariance Distance covariance Distance covariance Hilbert space Hilbert space Projection correlation Projection correlation Test of independence Test of independence
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| GB/T 7714 | Lai, Tingyu , Zhang, Zhongzhan , Wang, Yafei et al. Testing independence of functional variables by angle covariance [J]. | JOURNAL OF MULTIVARIATE ANALYSIS , 2021 , 182 . |
| MLA | Lai, Tingyu et al. "Testing independence of functional variables by angle covariance" . | JOURNAL OF MULTIVARIATE ANALYSIS 182 (2021) . |
| APA | Lai, Tingyu , Zhang, Zhongzhan , Wang, Yafei , Kong, Linglong . Testing independence of functional variables by angle covariance . | JOURNAL OF MULTIVARIATE ANALYSIS , 2021 , 182 . |
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摘要 ：
The functional linear quantile regression model is widely used to characterize the relationship between a scalar response and a functional covariate. Most existing research results are based on a correct assumption that the response is related to the functional predictor through a linear model for given quantile levels. This paper focuses on investigating the adequacy check of the functional linear quantile regression model. We propose a nonparametric U-process test statistic based on the functional principal component analysis. It is proved that the test statistic follows a normal distribution asymptotically under the null hypothesis and diverges to infinity for any misspecified models. Therefore, the test is consistent against any fixed alternative. Moreover, it is shown that the test has asymptotic power one for the, local alternative hypothetical models converging to the null hypothesis at the rates n(-1/2). The finite sample properties of the test statistic are illustrated through extensive simulation studies. A real data set of 24 hourly measurements of ozone levels in Sacramento, California is analyzed by the proposed test. (C) 2020 Elsevier B.V. All rights reserved.
关键词 ：
Quantile regression Quantile regression Hypothesis test Hypothesis test Kernel smoothing Kernel smoothing Functional linear models Functional linear models
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| GB/T 7714 | Shi, Gongming , Du, Jiang , Sun, Zhihua et al. Checking the adequacy of functional linear quantile regression model [J]. | JOURNAL OF STATISTICAL PLANNING AND INFERENCE , 2021 , 210 : 64-75 . |
| MLA | Shi, Gongming et al. "Checking the adequacy of functional linear quantile regression model" . | JOURNAL OF STATISTICAL PLANNING AND INFERENCE 210 (2021) : 64-75 . |
| APA | Shi, Gongming , Du, Jiang , Sun, Zhihua , Zhang, Zhongzhan . Checking the adequacy of functional linear quantile regression model . | JOURNAL OF STATISTICAL PLANNING AND INFERENCE , 2021 , 210 , 64-75 . |
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摘要 ：
Currently, working with partially observed functional data has attracted a greatly increasing attention, since there are many applications in which each functional curve may be observed only on a subset of a common domain, and the incompleteness makes most existing methods for functional data analysis ineffective. In this paper, motivated by the appealing characteristics of conditional quantile regression, the authors consider the functional linear quantile regression, assuming the explanatory functions are observed partially on dense but discrete point grids of some random subintervals of the domain. A functional principal component analysis (FPCA) based estimator is proposed for the slope function, and the convergence rate of the estimator is investigated. In addition, the finite sample performance of the proposed estimator is evaluated through simulation studies and a real data application.
关键词 ：
functional principal component analysis functional principal component analysis Conditional quantile regression Conditional quantile regression incomplete curves incomplete curves functional data analysis functional data analysis
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| GB/T 7714 | Xiao Juxia , Xie Tianfa , Zhang Zhongzhan . Estimation in Partially Observed Functional Linear Quantile Regression [J]. | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY , 2021 , 35 (1) : 313-341 . |
| MLA | Xiao Juxia et al. "Estimation in Partially Observed Functional Linear Quantile Regression" . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 35 . 1 (2021) : 313-341 . |
| APA | Xiao Juxia , Xie Tianfa , Zhang Zhongzhan . Estimation in Partially Observed Functional Linear Quantile Regression . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY , 2021 , 35 (1) , 313-341 . |
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摘要 ：
A novel metric, called kernel-based conditional mean dependence (KCMD), is proposed to measure and test the departure from conditional mean independence between a response variable Y and a predictor variable X, based on the reproducing kernel embedding and the Hilbert-Schmidt norm of a tensor operator. The KCMD has several appealing merits. It equals zero if and only if the conditional mean of Y given X is independent of X, i.e. E(Y vertical bar X) = E(Y) almost surely, provided that the employed kernel is characteristic; it can be used to detect all kinds of conditional mean dependence with an appropriate choice of kernel; it has a simple expectation form and allows an unbiased empirical estimator. A class of test statistics based on the estimated KCMD is constructed, and a wild bootstrap test procedure to the conditional mean independence is presented. The limit distributions of the test statistics and the bootstrapped statistics under null hypothesis, fixed alternative hypothesis and local alternative hypothesis are given respectively, and a data-driven procedure to choose a suitable kernel is suggested. Simulation studies indicate that the tests based on the KCMD have close powers to the tests based on martingale difference divergence in monotone dependence, but excel in the cases of nonlinear relationships or the moment restriction on X is violated. Two real data examples are presented for the illustration of the proposed method. (C) 2021 Elsevier B.V. All rights reserved.
关键词 ：
Functional data Functional data Hilbert-Schmidt norm Hilbert-Schmidt norm U-statistics U-statistics Conditional mean dependence Conditional mean dependence
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| GB/T 7714 | Lai, Tingyu , Zhang, Zhongzhan , Wang, Yafei . A kernel-based measure for conditional mean dependence [J]. | COMPUTATIONAL STATISTICS & DATA ANALYSIS , 2021 , 160 . |
| MLA | Lai, Tingyu et al. "A kernel-based measure for conditional mean dependence" . | COMPUTATIONAL STATISTICS & DATA ANALYSIS 160 (2021) . |
| APA | Lai, Tingyu , Zhang, Zhongzhan , Wang, Yafei . A kernel-based measure for conditional mean dependence . | COMPUTATIONAL STATISTICS & DATA ANALYSIS , 2021 , 160 . |
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