零膨胀计数数据函数型部分变系数模型

Functional Partially Varying Coefficient Model for Zero-inflated Count Data

在实际数据分析中经常会遇到零膨胀计数数据作为响应变量与函数型随机变量和随机向量作为预测变量相关联。本文考虑函数型部分变系数零膨胀模型(FPVCZIM),模型中无穷维的斜率函数用函数型主成分基逼近,系数函数用B-样条进行拟合。通过EM算法得到估计量,讨论其理论性质,在一些正则条件下获得了斜率函数和系数函数估计量的收敛速度。有限样本的Monte Carlo模拟研究和真实数据分析被用来解释本文提出的方法。

Actual data analysis frequently comes across the case where zero-inflated count response will be related to both a function-valued random variable and random vector as the predictor variables.Functional partially varying coefficient zero-inflated model(FPVCZIM)is discussed in the paper,and the infinite slope function is approximated by the principal component basis function and coefficient functions are fitted by Bspline.The expectation-maximization algorithm is used to obtain the estimators,and their theoretical properties are considered.The rates of convergency of the estimators of infinite slope function and coefficient functions are obtained under some regularity conditions,respectively.Both finite sample Monte Carlo simulation studies and real data analysis are used to illustrate our proposed method.