函数型可加模型的变量选择方法研究及其在人口年龄结构数据上的应用

Variable Selection for Functional Additive Models and an Application to the Population Age Structure Data

摘要: 本文主要研究因变量为标量,自变量为函数型变量的函数型可加模型的估计和变量选择问题.为了估计模型并简化模型结构, 本文提出三种估计函数型可加模型的方法,不仅可以对可加成分未知函数形式进行估计,还可以对可加成分进行选择，提高模型解释能力. 基于~2018~年~82~个经济体的截面数据,实证研究部分将对数起点人口占比曲线视为代表人口年龄结构的函数型自变量,建立起非寿险需求估计模型, 并得到如下结论:第一, 衰退型人口结构对非寿险需求存在推动作用;第二, 即将退休人口密度的增加对非寿险需求存在推动作用.

Abstract: In this paper, we study component selection and estimation for functional additive models, which involve a scalar response and a functional predictor. Three methods are proposed to achieve a much more parsimonious model structure with better interpretation. Based on a cross-sectional data of 82 economics in 2018, we build a non-life insurance demand model with age proportion log hazard curve of the population as functional independent variable. We found that the declining demographic structure and higher proportion of people who heading for retirement has negative impact on non-life insurance demand.