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学者姓名：张忠占
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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 ：
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 ：
Functional linear models Functional linear models Hypothesis test Hypothesis test Kernel smoothing Kernel smoothing Quantile regression Quantile regression
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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 . |
| 导入链接 | NoteExpress RIS BibTex |
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|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. © 2021
关键词 ：
Statistical tests Statistical tests Statistics Statistics
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| GB/T 7714 | Lai, Tingyu , Zhang, Zhongzhan , Wang, Yafei . A kernel-based measure for conditional mean dependence [J]. | Computational Statistics and Data Analysis , 2021 , 160 . |
| MLA | Lai, Tingyu et al. "A kernel-based measure for conditional mean dependence" . | Computational Statistics and Data Analysis 160 (2021) . |
| APA | Lai, Tingyu , Zhang, Zhongzhan , Wang, Yafei . A kernel-based measure for conditional mean dependence . | Computational Statistics and Data Analysis , 2021 , 160 . |
| 导入链接 | NoteExpress RIS BibTex |
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 ：
Conditional quantile regression Conditional quantile regression functional data analysis functional data analysis functional principal component analysis functional principal component analysis incomplete curves incomplete curves
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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 . |
| MLA | Xiao Juxia et al. "Estimation in Partially Observed Functional Linear Quantile Regression" . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY (2021) . |
| APA | Xiao Juxia , Xie Tianfa , Zhang Zhongzhan . Estimation in Partially Observed Functional Linear Quantile Regression . | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY , 2021 . |
| 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 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
在恒定应力部分加速寿命试验下,基于左删失样本,研究了逆Rayleigh分布的参数估计问题。运用极大似然法得到未知参数和加速因子的极大似然估计。根据Louis提出的缺失信息原则,计算了Fisher信息矩阵,得到分布参数和加速因子的近似置信区间。当取参数的先验分布为指数分布时,在平方损失函数下求得了参数的贝叶斯估计,并利用极大似然法估计了超参数。通过Monte Carlo模拟,得到估计量的均方误差,据此对极大似然估计和贝叶斯估计进行了比较。最后,计算了不同左删失样本下逆Rayleigh分布参数及加速因子的估计。
关键词 ：
左删失样本 左删失样本 加速因子 加速因子 部分加速寿命试验 部分加速寿命试验 极大似然估计 极大似然估计 逆Rayleigh分布 逆Rayleigh分布
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| GB/T 7714 | 龙兵 , 张忠占 . 左删失恒定应力部分加速寿命试验下逆Rayleigh分布的参数估计 [J]. | 浙江大学学报(理学版) , 2020 , 47 (03) : 315-321 . |
| MLA | 龙兵 et al. "左删失恒定应力部分加速寿命试验下逆Rayleigh分布的参数估计" . | 浙江大学学报(理学版) 47 . 03 (2020) : 315-321 . |
| APA | 龙兵 , 张忠占 . 左删失恒定应力部分加速寿命试验下逆Rayleigh分布的参数估计 . | 浙江大学学报(理学版) , 2020 , 47 (03) , 315-321 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
基于定时区间删失样本,研究了指数分布产品在恒定应力部分加速寿命试验下的参数估计。利用EM算法得到了分布参数和加速因子的迭代方程。根据Louis提出的缺失信息原则计算了Fisher信息矩阵。由极大似然估计的渐近正态性,构造出分布参数和加速因子的近似置信区间。通过Monte Carlo模拟,从平均相对误差和均方误差两方面对估计量进行了计算,结果表明所有的估计量都具有大样本性质。最后通过模拟样本,计算了不同应力水平下分布参数、加速因子和可靠度的估计。
关键词 ：
加速因子 加速因子 定时区间删失试验 定时区间删失试验 指数分布 指数分布 极大似然估计 极大似然估计 部分加速寿命试验 部分加速寿命试验
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| GB/T 7714 | 龙兵 , 张忠占 . 恒定应力部分加速寿命试验的可靠性分析 [J]. | 火力与指挥控制 , 2020 , 45 (01) : 53-58,64 . |
| MLA | 龙兵 et al. "恒定应力部分加速寿命试验的可靠性分析" . | 火力与指挥控制 45 . 01 (2020) : 53-58,64 . |
| APA | 龙兵 , 张忠占 . 恒定应力部分加速寿命试验的可靠性分析 . | 火力与指挥控制 , 2020 , 45 (01) , 53-58,64 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
We propose randomized inference (RI), a new statistical inference approach. RI may be realized through a randomized estimate (RE) of a parameter vector, which is a random vector that takes values in the parameter space with a probability density function (PDF) that depends on the sample or sufficient statistics, such as the posterior distributions in Bayesian inference. Based on the PDF of an RE of an unknown parameter, we propose a framework for both the vertical density representation (VDR) test and the construction of a confidence region. This approach is explained with the aid of examples. For the equality hypothesis of multiple normal means without the condition of variance homogeneity, we present an exact VDR test, which is shown as an extension of one-way analysis of variance (ANOVA). In the case of two populations, the PDF of the Welch statistics is given using RE. Furthermore, through simulations, we show that the empirical distribution function, the approximatedt, and the RE distribution function of Welch statistics are almost equal. The VDR test of the homogeneity of variance is shown to be more efficient than both the Bartlett test and the revised Bartlett test. Finally, we discuss the prospects of RI.
关键词 ：
confidence distribution confidence distribution pivot pivot randomized inference randomized inference VDR test VDR test vertical density representation vertical density representation
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| GB/T 7714 | Zhang, Zhongzhan , Dai, Jiajia , Yang, Zhenhai . Randomized statistical inference: A unified statistical inference frame of frequentist, fiducial, and Bayesian inference [J]. | SCIENCE CHINA-MATHEMATICS , 2020 , 63 (5) : 1007-1028 . |
| MLA | Zhang, Zhongzhan et al. "Randomized statistical inference: A unified statistical inference frame of frequentist, fiducial, and Bayesian inference" . | SCIENCE CHINA-MATHEMATICS 63 . 5 (2020) : 1007-1028 . |
| APA | Zhang, Zhongzhan , Dai, Jiajia , Yang, Zhenhai . Randomized statistical inference: A unified statistical inference frame of frequentist, fiducial, and Bayesian inference . | SCIENCE CHINA-MATHEMATICS , 2020 , 63 (5) , 1007-1028 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Statistical inferences under simple stochastic ordering for two continuous populations has a long and rich history. But further study for multiple populations is still expected. In this article, we consider samples test for simple stochastic ordering against unrestricted alternative. A test statistic is constructed with the empirical distribution functions and the isotonic regression estimates of distribution functions, and the null asymptotic distribution of the proposed test statistic is given. A bootstrap procedure is suggested for the critical values, and some simulation results are presented to illustrate the proposed test method.
关键词 ：
bootstrap critical values bootstrap critical values isotonic regression estimator isotonic regression estimator multi-samples test multi-samples test Simple stochastic ordering Simple stochastic ordering
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| GB/T 7714 | Zhang, Jianling , Zhang, Zhongzhan . Nonparametric multi-samples test for simple stochastic ordering against unrestricted alternative [J]. | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2020 . |
| MLA | Zhang, Jianling et al. "Nonparametric multi-samples test for simple stochastic ordering against unrestricted alternative" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS (2020) . |
| APA | Zhang, Jianling , Zhang, Zhongzhan . Nonparametric multi-samples test for simple stochastic ordering against unrestricted alternative . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2020 . |
| 导入链接 | NoteExpress RIS BibTex |
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