In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown smooth regression parameter function that varies with the level of quantile. The objective is to test that the regression parameter is constant across several quantile levels of interest. The parameter function is estimated by combining ideas from functional principal component analysis and quantile regression. An adjusted Wald testing procedure is proposed for this hypothesis of interest, and its chi-square asymptotic null distribution is derived. The testing procedure is investigated numerically in simulations involving sparse and noisy functional covariates and in a capital bike share data application. The proposed approach is easy to implement and the {\tt R} code is published online at \url{https://github.com/xylimeng/fQR-testing}.

翻译：在本文中,我们研究对斜体反应和函数共变的功能微量回归的统计推论。 具体地说, 我们考虑一个功能性线性微量回归模型, 该模型通过函数共变和未知的平滑回归参数函数之间的内产物模型模型来模拟共变数对响应的四分位数的影响, 且该参数参数功能性微量回归值的功能性微量回归值与函数性共变数的函数值不同。 目的是测试回归参数参数参数参数在几个微量水平上是恒定的。 参数函数函数函数函数函数通过将功能性主要成分分析的理念和参数性回归值的回归值结合来估算。 对这一利益假设提出了调整的 Wald 测试程序, 并得出了其 ir- siquare asymptaty natal分布。 测试程序在涉及分散和吵闹的功能共变和资本自行车共享数据应用的模拟中进行数字调查。 拟议的方法容易执行, 并在\url{ https://github. com/ xylimeng/ f- QR- 测试中在线公布 代码。