Model selection and structure specification in ultra-high dimensional generalised semi-varying coefficient models
超高维广义半变系数模型的模型选择与结构识别AI 解读 ↓
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超高维广义半变系数模型的模型选择与结构识别
- 研究问题
- 当候选协变量多于样本量时，如何在广义半变系数模型中筛选重要变量，并区分入选变量的常系数与变系数结构？
- 方法与思路
- 作者先用 LASSO 惩罚似然得到初估，再结合局部似然二次近似与自适应组 LASSO 或组 SCAD 构造惩罚加权最小二乘。
- 材料陈述的贡献
- 摘要称，该程序可同时选择变量与识别常系数结构，提供计算算法，并在一定条件下具有稀疏性和 oracle 性质。
- 阅读关注点
- 应核对维度增长、信号强度和光滑性条件，初估如何影响后续选择，以及调参规则、结构识别与 oracle 性质的含义。
- 阅读边界
- 仅据稿件版本未注明的 OpenAlex 摘要，所谓温和条件及模拟数值未说明；计算吸引力和实证发现不能据此作一般优越性判断。
原文摘要
In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size. We first propose a penalised likelihood method with the LASSO penalty function to obtain the preliminary estimates of the functional coefficients. Then, using the quadratic approximation for the local log-likelihood function and the adaptive group LASSO penalty (or the local linear approximation of the group SCAD penalty) with the help of the preliminary estimation of the functional coefficients, we introduce a novel penalised weighted least squares procedure to select the significant covariates and identify the constant coefficients among the coefficients of the selected covariates, which could thus specify the semiparametric modelling structure. The developed model selection and structure specification approach not only inherits many nice statistical properties from the local maximum likelihood estimation and nonconcave penalised likelihood method, but also computationally attractive thanks to the computational algorithm that is proposed to implement our method. Under some mild conditions, we establish the asymptotic properties for the proposed model selection and estimation procedure such as the sparsity and oracle property. We also conduct simulation studies to examine the finite sample performance of the proposed method, and finally apply the method to analyse a real data set, which leads to some interesting findings.