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学者姓名：张忠占
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Abstract ：
This paper is focused on the specification test of functional linear quantile regression models. A nonparametric test statistic is proposed based on the orthogonality of residual and its conditional expectation. It is proved with mild assumptions that the proposed statistic follows asymptotically the standard normal distribution under the null hypothesis, but tends to infinity under alternative hypothesis. The asymptotic power of the test is also presented for some local alternative hypotheses. The test is easy to implement, and is shown by simulations powerful even for small sample sizes. A real data example with the Capital Bikeshare data is presented for illustration.
Keyword ：
Model specification Model specification Quadratic form Quadratic form Functional data Functional data Nonparametric test Nonparametric test Quantile regression Quantile regression
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| GB/T 7714 | Xia, Lili , Zhang, Zhongzhan , Shi, Gongming . A consistent specification test for functional linear quantile regression models [J]. | STATISTICS AND ITS INTERFACE , 2024 , 17 (4) : 649-667 . |
| MLA | Xia, Lili 等. "A consistent specification test for functional linear quantile regression models" . | STATISTICS AND ITS INTERFACE 17 . 4 (2024) : 649-667 . |
| APA | Xia, Lili , Zhang, Zhongzhan , Shi, Gongming . A consistent specification test for functional linear quantile regression models . | STATISTICS AND ITS INTERFACE , 2024 , 17 (4) , 649-667 . |
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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 ：
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 ：
本文研究了函数型二次回归中二次参数函数的显著性检验问题.采用函数型主成分分析将预测变量函数进行投影降维,利用零模型和全模型的残差平方和构造F型检验统计量.在一定的正则条件下证明了检验统计量在原假设下渐近于F分布,在备择假设下检验统计量依概率趋于无穷,从而表明该检验方法是相合的.进一步证明了在一定收敛速度的局部备择假设下,检验统计量渐近于非中心F分布.最后通过数值模拟研究了该检验方法在有限样本下的表现,并给出了一个实际例子进一步验证所提方法的有效性.
Keyword ：
函数型二次回归 函数型二次回归 渐近分布 渐近分布 函数型主成分分析 函数型主成分分析 局部备择假设 局部备择假设 F型检验 F型检验
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| GB/T 7714 | 李海昕 , 肖菊霞 , 张忠占 . 函数型二次模型的假设检验 [J]. | 数理统计与管理 , 2023 , 42 (1) : 45-64 . |
| MLA | 李海昕 等. "函数型二次模型的假设检验" . | 数理统计与管理 42 . 1 (2023) : 45-64 . |
| APA | 李海昕 , 肖菊霞 , 张忠占 . 函数型二次模型的假设检验 . | 数理统计与管理 , 2023 , 42 (1) , 45-64 . |
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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 ：
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 et al. "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 ：
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.
Keyword ：
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
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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 . |
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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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