Inference in functional linear quantile regression
Inference in functional linear quantile regression
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DOI：
10.1016/j.jmva.2022.104985
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发表时间：
2016-02
影响因子：
1.6
通讯作者：
M. Li;K. Wang;A. Maity;A. Staicu
中科院分区：
文献类型：
--
作者：
M. Li;K. Wang;A. Maity;A. Staicu
在本文中，我们研究标量响应和函数协变量的函数分位数回归中的统计推断。具体来说，我们考虑一个函数线性分位数回归模型，其中协变量对响应分位数的影响是通过函数协变量与随分位数水平变化的未知平滑回归参数函数之间的内积来建模的。目的是测试回归参数在多个感兴趣的分位数水平上是否恒定。参数函数的估计结合了函数主成分分析和分位数回归的思想。针对这一感兴趣的假设提出了调整后的 Wald 检验程序，并推导了其卡方渐近零分布。在涉及稀疏和噪声函数协变量的模拟以及资本自行车共享数据应用中对测试过程进行了数值研究。所提出的方法很容易实现，并且 Rcode 在线发布于 https://github.com/xylimeng/fQR-testing。
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 theRcode is published online at https://github.com/xylimeng/fQR-testing.