In this paper, we develop statistical inference procedures for functional quadratic quantile regression model in which the response is a scalar and the predictor is a random function defined on a compact set of R . The functional coefficients are estimated by functional principal components. The asymptotic properties of the resulting estimators are established under mild conditions. In order to test the significance of the nonlinear term in the model, we propose a rank score test procedure. The asymptotic properties of the proposed test statistic are established. The proposed method provides a highly efficient and robust alternative to the least squares method, and can be conveniently implemented using existing R software package. Finally, we examine the performance of the proposed method for finite sample sizes by Monte Carlo simulation studies and illustrate it with a real data example.

中文翻译：

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函数二次分位数回归模型的统计推断

在本文中，我们为函数二次分位数回归模型开发了统计推断程序，其中响应是标量，预测变量是定义在 R 的紧凑集上的随机函数。函数系数由函数主成分估计。所得估计量的渐近性质是在温和条件下建立的。为了测试模型中非线性项的显着性，我们提出了等级评分测试程序。建立了所提出的检验统计量的渐近特性。所提出的方法为最小二乘法提供了一种高效且稳健的替代方法，并且可以使用现有的 R 软件包方便地实现。最后，