Motivated by the study of how daily temperature affects soybean yield, this article proposes a simultaneous functional quantile regression (FQR) model featuring a locally sparse bivariate slope function indexed by both quantile and time and linked to a functional predictor. The slope function's local sparsity means it holds non-zero values only in certain segments of its domain, remaining zero elsewhere. These zero-slope regions, which vary by quantile, indicate times when the functional predictor has no discernible impact on the response variable. This feature boosts the model's interpretability. Unlike traditional FQR models, which fit one quantile at a time and have several limitations, our proposed method can handle a spectrum of quantiles simultaneously. We tested the new approach through simulation studies, demonstrating its clear advantages over standard techniques. To validate its practical use, we applied the method to soybean yield data, pinpointing the time periods when daily temperature doesn't affect yield. This insight could be crucial for agricultural planning and crop management.

翻译：本文受研究日温度如何影响大豆产量的启发，提出了一种同步函数型分位数回归模型。该模型具有一个局部稀疏的双变量斜率函数，该函数同时以分位数和时间作为索引，并与一个函数型预测变量相关联。斜率函数的局部稀疏性意味着其仅在其定义域的某些区间内取非零值，而在其余区域保持为零。这些零斜率区域随分位数变化而变化，指示了函数型预测变量对响应变量无明显影响的时间段。这一特性增强了模型的可解释性。与传统的函数型分位数回归模型（一次仅拟合一个分位数且存在若干局限性）不同，我们提出的方法能够同时处理一系列分位数。我们通过模拟研究测试了新方法，证明了其相较于标准技术的明显优势。为验证其实际应用价值，我们将该方法应用于大豆产量数据，精确识别了日温度对产量无影响的时间段。这一发现可能对农业规划和作物管理至关重要。