New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models
半参数变系数部分线性模型的新型高效估计与变量选择方法AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确以分位数回归及复合分位数回归估计参数和变系数函数，直接对应分位数方法。
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半参数变系数部分线性模型的新型高效估计与变量选择方法
- 研究问题
- 在同时包含变系数函数和参数回归系数的半参数模型中，如何兼顾估计效率、分位数分析与高维协变量的稀疏选择？
- 方法与思路
- 作者先研究分位数回归，再构造半参数复合分位数回归，并引入自适应惩罚进行变量选择，以模拟和血浆β胡萝卜素数据展示。
- 材料陈述的贡献
- 摘要称估计量具有渐近正态性和最佳收敛速率，惩罚方法具有预言性质，并报告多种非正态误差下相对最小二乘的效率优势。
- 阅读关注点
- 应核对复合分位数的构造、效率比较的误差分布条件、参数与函数部分的不同渐近尺度，以及预言性质对维度和调参的要求。
- 阅读边界
- 仅据OpenAlex索引摘要，稿件版本未注明；摘要给出的效率损失上界与优势须结合全文条件理解，不能推广至任意误差或维度。
原文摘要
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the semiparametric varying-coefficient partially linear model. We first study quantile regression estimates for the nonparametric varying-coefficient functions and the parametric regression coefficients. To achieve nice efficiency properties, we further develop a semiparametric composite quantile regression procedure. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the estimators achieve the best convergence rate. Moreover, we show that the proposed method is much more efficient than the least-squares-based method for many non-normal errors and that it only loses a small amount of efficiency for normal errors. In addition, it is shown that the loss in efficiency is at most 11.1% for estimating varying coefficient functions and is no greater than 13.6% for estimating parametric components. To achieve sparsity with high-dimensional covariates, we propose adaptive penalization methods for variable selection in the semiparametric varying-coefficient partially linear model and prove that the methods possess the oracle property. Extensive Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. Finally, we apply the new methods to analyze the plasma beta-carotene level data.