Changes on temperature patterns, on a local scale, are perceived by individuals as the most direct indicators of global warming and climate change. As a specific example, for an Atlantic climate location, spring and fall seasons should present a mild transition between winter and summer, and summer and winter, respectively. By observing daily temperature curves along time, being each curve attached to a certain calendar day, a regression model for these variables (temperature curve as covariate and calendar day as response) would be useful for modeling their relation for a certain period. In addition, temperature changes could be assessed by prediction and observation comparisons in the long run. Such a model is presented and studied in this work, considering a nonparametric Nadaraya-Watson-type estimator for functional covariate and circular response. The asymptotic bias and variance of this estimator, as well as its asymptotic distribution are derived. Its finite sample performance is evaluated in a simulation study and the proposal is applied to investigate a real-data set concerning temperature curves.
翻译:在局部范围内,个人认为温度模式的变化是全球升温和气候变化的最直接指标。作为具体例子,大西洋气候地点的春季和秋季季节应分别显示冬季和夏季、夏季和冬季之间的温适过渡。通过在时间上观测日温曲线,即附于某一日历日的每个曲线,这些变量的回归模型(温度曲线作为共变曲线和日历日作为响应)将有助于在一定时期内模拟其关系。此外,温度变化可以通过长期的预测和观测比较加以评估。在这项工作中提出并研究了这样一个模型,其中考虑到功能性共变和圆形反应的非对称Nadaraya-Watson型天命测算仪。该测算仪的偏差和偏差,以及该测算仪的分布。模拟研究对它的有限样本性性能进行了评估,并应用该提案来调查关于温度曲线的一套真实数据。