This paper investigates the hypothesis test of the parametric component in partial functional linear quantile regression model in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. A quantile rank score test based on functional principal component analysis is developed. Under mild conditions, we establish the consistency of the proposed test statistic, and show that the proposed test can detect Pitman local alternatives converging to the null hypothesis at the usual parametric rate. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. Finally, an illustrative example is given through fitting the Berkeley growth data and testing the effect of gender on the height of kids.

本文研究了部分函数线性分位数回归模型中参数分量的假设检验，在该模型中，因变量与有限长度向量和作为预测变量的函数值随机变量都相关。开发了基于功能主成分分析的分位数等级测试。在温和的条件下，我们建立了拟议的检验统计量的一致性，并表明拟议的检验可以检测出以通常的参数速率收敛到零假设的Pitman局部替代方案。仿真研究表明，所提出的测试程序在有限的样本量下具有良好的大小和功效。最后，通过拟合伯克利成长数据并测试性别对孩子身高的影响，给出了一个说明性例子。