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学者姓名：张忠占
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Abstract ：
Model checking methods based on non-parametric estimation are widely used because of their tractable limiting null distributions and being sensitive to high-frequency oscillation alternative models. However, this kind of test suffers from the curse of dimensionality, resulting in slow convergence, especially for functional data with infinite dimensional features. In this paper, we propose an adaptive-to-model test for a parametric functional single-index model by using the orthogonality of residual and its conditional expectation. The test achieves model adaptation by sufficient dimension reduction which utilizes functional sliced inverse regression. This test procedure can be easily extended to other non-parametric test methods. Under certain conditions, we prove the asymptotic properties of the test statistic under the null hypothesis, fixed alternative hypothesis and local alternative hypothesis. Simulations show that our test has better performance than the method that does not use functional sufficient dimension reduction. An analysis of COVID-19 data verifies our conclusion.
Keyword ：
functional data functional data model checking model checking sufficient dimension reduction sufficient dimension reduction sliced inverse regression sliced inverse regression single-index model single-index model
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| GB/T 7714 | Xia, Lili , Lai, Tingyu , Zhang, Zhongzhan . An Adaptive-to-Model Test for Parametric Functional Single-Index Model [J]. | MATHEMATICS , 2023 , 11 (8) . |
| MLA | Xia, Lili 等. "An Adaptive-to-Model Test for Parametric Functional Single-Index Model" . | MATHEMATICS 11 . 8 (2023) . |
| APA | Xia, Lili , Lai, Tingyu , Zhang, Zhongzhan . An Adaptive-to-Model Test for Parametric Functional Single-Index Model . | MATHEMATICS , 2023 , 11 (8) . |
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Abstract ：
This article is focused on the problem to measure and test the conditional mean dependence of a response variable on a predictor variable. A local influence detection approach is developed combining with the martingale difference divergence (MDD) metric, and an efficient wild bootstrap implementation is given. The obtained new metric of the conditional mean dependence holds the merits of MDD, while it is more sensitive than the original one, and leads to a powerful test to nonlinear relationships. It is shown by simulations that the proposed test can achieve higher power for general conditional mean dependence relationships even in high-dimensional settings. Theoretical asymptotic properties of the local influence test statistic are given, and a real data analysis is also presented for further illustration. The localization idea could be combined with other conditional mean dependence metrics.
Keyword ：
Nonlinear dependence Nonlinear dependence Conditional mean independence Conditional mean independence Local influence Local influence Martingale difference divergence Martingale difference divergence
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| GB/T 7714 | Lai, Tingyu , Zhang, Zhongzhan . Local Influence Detection of Conditional Mean Dependence [J]. | COMMUNICATIONS IN MATHEMATICS AND STATISTICS , 2023 . |
| MLA | Lai, Tingyu 等. "Local Influence Detection of Conditional Mean Dependence" . | COMMUNICATIONS IN MATHEMATICS AND STATISTICS (2023) . |
| APA | Lai, Tingyu , Zhang, Zhongzhan . Local Influence Detection of Conditional Mean Dependence . | COMMUNICATIONS IN MATHEMATICS AND STATISTICS , 2023 . |
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Abstract ：
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.
Keyword ：
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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Abstract ：
In this paper, we first investigate a new asymmetric Huber regression (AHR) estimation procedure to analyze skewed data with partial functional linear models. To automatically reflect distributional features as well as bound the influence of outliers effectively, we further propose a weighted composite asymmetric Huber regression (WCAHR) estimation procedure by combining the strength across multiple asymmetric Huber loss functions. The slope function and constant coefficients are estimated through minimizing the combined loss function and approximating the slope function with principal component analysis. The asymptotic properties of the proposed estimators are derived. To realize the WCAHR estimation, we also develop a practical algorithm based on pseudo data. Numerical results show that the proposed WCAHR estimators can well adapt to the different error distributions, and thus are more useful in practice. Two real data examples are presented to illustrate the applications of the proposed methods.
Keyword ：
weighted composite asymmetric Huber regression weighted composite asymmetric Huber regression functional principal component analysis functional principal component analysis asymmetric Huber regression asymmetric Huber regression functional data analysis functional data analysis partial functional linear model partial functional linear model
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| GB/T 7714 | Xiao, Juxia , Yu, Ping , Zhang, Zhongzhan . Weighted composite asymmetric Huber estimation for partial functional linear models [J]. | AIMS MATHEMATICS , 2022 , 7 (5) : 7657-7684 . |
| MLA | Xiao, Juxia 等. "Weighted composite asymmetric Huber estimation for partial functional linear models" . | AIMS MATHEMATICS 7 . 5 (2022) : 7657-7684 . |
| APA | Xiao, Juxia , Yu, Ping , Zhang, Zhongzhan . Weighted composite asymmetric Huber estimation for partial functional linear models . | AIMS MATHEMATICS , 2022 , 7 (5) , 7657-7684 . |
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Abstract ：
Doubly robust (DR) methods that employ both the propensity score and outcome models are widely used to estimate the causal effect of a treatment and generally outperform those methods only using the propensity score or the outcome model. However, without appropriately chosen the working models, DR estimators may substantially lose efficiency. In this paper, based on the augmented inverse probability weighting procedure, we derive a new estimating equation for the causal effect by the strategy of combining estimating equations. The resulting estimator by solving the new estimating equation retains doubly robust and can improve the efficiency under the misspecification of conditional mean working model. We further show the large sample properties of the proposed estimator under some regularity conditions. Through simulation experiments and a real data analysis, we illustrate that the proposed method is competitive with its competitors, which is in line with those implied by the asymptotic theory.
Keyword ：
Doubly robust method Doubly robust method Average treatment effect Average treatment effect Inverse probability weighting Inverse probability weighting Estimating equation Estimating equation Causal effect Causal effect Semiparametric efficiency Semiparametric efficiency
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| GB/T 7714 | Wei, Shaojie , Li, Gaorong , Zhang, Zhongzhan . An Alternative Doubly Robust Estimation in Causal Inference Model [J]. | COMMUNICATIONS IN MATHEMATICS AND STATISTICS , 2022 . |
| MLA | Wei, Shaojie 等. "An Alternative Doubly Robust Estimation in Causal Inference Model" . | COMMUNICATIONS IN MATHEMATICS AND STATISTICS (2022) . |
| APA | Wei, Shaojie , Li, Gaorong , Zhang, Zhongzhan . An Alternative Doubly Robust Estimation in Causal Inference Model . | COMMUNICATIONS IN MATHEMATICS AND STATISTICS , 2022 . |
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Abstract ：
As extensions of means, expectiles embrace all the distribution information of a random variable. The expectile regression is computationally friendlier because the asymmetric least square loss function is differentiable everywhere. This regression also enables effective estimation of the expectiles of a response variable when potential explanatory variables are given. In this study, we propose the partial functional linear expectile regression model. The slope function and constant coefficients are estimated by using the functional principal component basis. The convergence rate of the slope function and the asymptotic normality of the parameter vector are established. To inspect the effect of the parametric component on the response variable, we develop Wald-type and expectile rank score tests and establish their asymptotic properties. The finite performance of the proposed estimators and test statistics are evaluated through simulation study. Results indicate that the proposed estimators are comparable to competing estimation methods and the newly proposed expectile rank score test is useful. The methodologies are illustrated by using two real data examples.
Keyword ：
Wald-type test Wald-type test expectile regression expectile regression functional principal component analysis functional principal component analysis heteroscedasticity heteroscedasticity expectile rank score test expectile rank score test
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| GB/T 7714 | Xiao, Juxia , Yu, Ping , Song, Xinyuan et al. Statistical inference in the partial functional linear expectile regression model [J]. | SCIENCE CHINA-MATHEMATICS , 2022 , 65 (12) : 2601-2630 . |
| MLA | Xiao, Juxia et al. "Statistical inference in the partial functional linear expectile regression model" . | SCIENCE CHINA-MATHEMATICS 65 . 12 (2022) : 2601-2630 . |
| APA | Xiao, Juxia , Yu, Ping , Song, Xinyuan , Zhang, Zhongzhan . Statistical inference in the partial functional linear expectile regression model . | SCIENCE CHINA-MATHEMATICS , 2022 , 65 (12) , 2601-2630 . |
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Abstract ：
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.
Keyword ：
Distance covariance Distance covariance Angle covariance Angle 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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Abstract ：
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.
Keyword ：
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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Abstract ：
响应变量删失时函数型部分线性分位数回归模型的估计
Keyword ：
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 . |
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Abstract ：
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.
Keyword ：
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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