Semiparametric quantile estimation for varying coefficient partially linear measurement errors models

Zhang, Jun; Zhou, Yan; Cui, Xia; Xu, Wangli

doi:10.1214/17-bjps357

Cited by 7 publications

(3 citation statements)

References 53 publications

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“…The varying coefficient model (2) has been well studied via various estimation methods, see for example, Hastie and Tibshirani (1993), Fan and Zhang (1999); Li, Li, Lian, and Tong (2017); Zhao and Lian (2016), Yang, Li, and Peng (2014), Li, Feng, and Peng (2011), Li, Xue, and Lian (2011); Zhang and Peng (2010); Lv, Fan, Lian, Suzuki, and Fukumizu (2020), Zhang, Zhou, Xu, and Li (2018), Zhao, Peng, and Huang (2018), Lian (2015), Lian, Lai, and Liang (2013), Fan and Huang (2005). In this paper, we adopt the local linear regression technique (Fan & Huang, 2005) to estimate

\left({\gamma}_0(u),{\gamma}_1(u),\dots, {\gamma}_q(u)\right)

in model (2) as an illustration.…”

Section: Estimation Methods and Asymptotic Resultsmentioning

confidence: 99%

Linear regression models with multiplicative distortions under new identifiability conditions

Zhang

Lin

Zhou

2023

Statistica Neerlandica

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This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. We propose new identifiability conditions for the distortion functions via the varying coefficient models, then moment‐based estimators of parameters in the model are proposed by using the estimated varying coefficient functions. This method does not require the independence condition between the confounding variables and the unobserved response and variables. We establish the connections among the varying coefficient based estimators, the conditional mean calibration and the conditional absolute mean calibration. We study the asymptotic results of these proposed estimators, and discuss their asymptotic efficiencies. Lastly, we make some comparisons among the proposed estimators through the simulation. These methods are applied to analyze a real dataset for an illustration.

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\left({\gamma}_0(u),{\gamma}_1(u),\dots, {\gamma}_q(u)\right)

in model (2) as an illustration.…”

Section: Estimation Methods and Asymptotic Resultsmentioning

confidence: 99%

Linear regression models with multiplicative distortions under new identifiability conditions

Zhang

Lin

Zhou

2023

Statistica Neerlandica

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“…In this study, we consider the combination of magnitude and shape outliers. In the case of outliers, the LS or maximum likelihood-based estimation methods produce biased estimates; thus, predictions obtained from the fitted model become unreliable (see, e.g., Zhang et al 2018). To overcome this issue, several robust methods have been proposed in functional regression models.…”

Section: Introductionmentioning

confidence: 99%

A partial least squares approach for function-on-function interaction regression

Beyaztaş

Shang

2021

Comput Stat

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The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical applications. In addition, these methods may be severely affected by such observations, leading to undesirable estimation and prediction results. A robust estimation method, based on iteratively reweighted simple partial least squares, is introduced to improve the prediction accuracy of the function-on-function linear regression model in the presence of outliers. The performance of the proposed method is based on the number of partial least squares components used to estimate the function-on-function linear regression model. Thus, the optimum number of components is determined via a data-driven error criterion. The finite-sample performance of the proposed method is investigated via several Monte Carlo experiments and an empirical data analysis. In addition, a nonparametric bootstrap method is applied to construct pointwise prediction intervals for the response function. The results are compared with some of the existing methods to illustrate the improvement potentially gained by the proposed method.

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“…的数据下, 复合期望分位数估计以及模型的应用. Zhang 等 [38] 给出了半参数变系数测量误差分位数回归模型的估计方法. Truquet [39] 对含时间变系数的线性模型进行了有效的半参数统计推断.…”

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Semiparametric varying-coefficient expectile model for estimating value at risk on dependent samples

Wang¹,

Yong²,

Zeng³

2021

Sci. Sin.-Math.

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关键词 α-混合半参数变系数期望分位数在险价值三阶段估计 MSC (2020) 主题分类 62G05, 91G70 1 引言风险度量建模一直是统计学和金融计量学中重要的研究议题和前沿问题. 获得诺贝尔奖的美国经济学家 Markowitz [1] 在投资组合理论中, 首次提出了收益与风险的度量理论, 即期望代表收益与方差代表风险的度量方法, 从而开创了风险的量化时代. 随后以 Black 和 Scholes [2] 的资产定价理论为标王子剑等: 相依样本下半参数变系数期望分位数风险度量模型统计推断志, 风险度量推动了金融计量学与风险管理的发展. 此外发展出更多风险管理的方法, 包括著名的一般均衡理论 [3, 4] 和保费均衡原则 [5] 等. 根据风险度量的侧重点不同, 可以将常用的风险度量分为两大类: 基于矩的风险度量和基于分位点的风险度量. 有关矩的风险度量主要有方差 (variance)、半方差 (semi-variance)、绝对离差 (absolute deviation)、半绝对离差 (semi-absolute deviation)、低位部分矩 (lower partial moments, LPM) 和 G-均值等. 有关矩的风险度量, 主要采用概率统计中表示离散程度的矩 (moment) 来度量金融资产或投资组合的风险, 波动性越强, 风险越大. 另一类则是以风险价值 (value at risk, VaR) 和期望损益 (expected shortfall, ES) 为代表的分位数 (quantile) 风险度量. 风险价值和期望损益是资产组合常用的两个风险度量工具, 其中 VaR 是被如巴塞尔委员会等众多国外的金融机构所认可和提倡的风险度量方法.

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Semiparametric quantile estimation for varying coefficient partially linear measurement errors models

Cited by 7 publications

References 53 publications

Linear regression models with multiplicative distortions under new identifiability conditions

Linear regression models with multiplicative distortions under new identifiability conditions

A partial least squares approach for function-on-function interaction regression

Semiparametric varying-coefficient expectile model for estimating value at risk on dependent samples

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