Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates
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协变量维数增长时相关数据的广义可加部分线性模型估计与选择
- 研究问题
- 当线性协变量与非线性分量都随样本量增加，且数据存在相关性、似然难以指定时，如何估计并选择模型？
- 方法与思路
- 作者以二次推断函数估计线性系数及非参数函数，并采用双重惩罚同时选择非零线性分量和非参数分量。
- 材料陈述的贡献
- 摘要称建立线性估计的渐近正态性、非参数收敛率和选择程序的渐近 oracle 性质，并报告模拟及肾癌药代应用。
- 阅读关注点
- 应核对维数增长率、相关结构的使用方式、函数平滑与惩罚条件，以及 oracle 性质对信号强度的要求。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；效率与功效改善的比较条件、增长率限制及中等样本模拟数值均未提供。
原文摘要
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases statistical power for correlated data through incorporating the correlation information. A unique feature of the proposed method is its capability of handling model selection in cases where it is difficult to specify the likelihood function. We derive the quadratic inference function-based estimators for the linear coefficients and the nonparametric functions when the dimension of covariates diverges, and establish asymptotic normality for the linear coefficient estimators and the rates of convergence for the nonparametric functions estimators for both finite and high-dimensional cases. The proposed method and theoretical development are quite challenging since the numbers of linear covariates and nonlinear components both increase as the sample size increases. We also propose a doubly penalized procedure for variable selection which can simultaneously identify nonzero linear and nonparametric components, and which has an asymptotic oracle property. Extensive Monte Carlo studies have been conducted and show that the proposed procedure works effectively even with moderate sample sizes. A pharmacokinetics study on renal cancer data is illustrated using the proposed method.