标题： 比较回归曲线——一个$L^1$点的观点 显示英文标题

标题： Comparing regression curves -- an $L^1$-point of view

摘要： 在本文中，我们通过测量两条回归曲线之间的面积来比较它们的差异，该面积由它们的$L^1$-距离表示。 我们为此度量开发了渐近置信区间，并进行了统计检验以研究两条曲线的相似性/等价性。 开发了专门用于等价性检验的引导方法，以获得具有良好小样本性质的程序，并严格证明了其一致性。 通过一个小的模拟研究来探讨了小样本性质。 显示英文摘要

摘要： In this paper we compare two regression curves by measuring their difference by the area between the two curves, represented by their $L^1$-distance. We develop asymptotic confidence intervals for this measure and statistical tests to investigate the similarity/equivalence of the two curves. Bootstrap methodology specifically designed for equivalence testing is developed to obtain procedures with good finite sample properties and its consistency is rigorously proved. The finite sample properties are investigated by means of a small simulation study.