响应变量删失时函数型部分线性分位数回归模型的估计

Estimation of Functional Partially Linear Quantile Regression Model with Censored Response

最近几年,函数型数据分析的理论和应用飞速发展.在许多实际应用里,响应变量往往存在随机右删失的情况.考虑利用函数型部分线性分位数回归模型来刻画函数型和标量预测量与右删失响应变量之间的关系.基于函数型主成分基函数来逼近未知的斜率函数,通过极小化逆概率加权分位数损失函数得到未知系数的估计量.文章的估计方法容易通过加权分位数回归程序实现.在一定的假设条件下,给出了有限维参数估计量的渐近正态性与斜率函数估计量的收敛速度.最后,通过模拟计算与应用实例证明了所提方法的有效性.

The theories and applications of functional data analysis have grown rapidly in recent years.In many applications,the scalar response variable which is subjected to randomly right censoring and functional covariates are increasingly encountered.This paper considers the functional partially linear quantile regression model to characterize the association between censored survival time and a set of functional and scalar predictors,and focuses the estimation of the unknown coefficients of the predictors.The proposed estimation method is based on functional principle component basis expansion of the unknown slope functional coefficient.It is easy to implement via existing weighted quantile regression procedure.The asymptotic normality of the estimator of finite-dimensional parameter as well as the rate of convergence for the estimator of slope function are established.Finally,the finite sample performance of the estimators is illustrated via the extensive simulation studies and a real data analysis.