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.

翻译：本文通过测量两条回归曲线之间的面积差（以$L^1$距离表示）来比较两条回归曲线。我们针对该测量指标开发了渐近置信区间，并设计了统计检验以探究两条曲线的相似性/等价性。专门为等价性检验设计的Bootstrap方法被建立，以获得具有良好有限样本性质的程序，并严格证明了其一致性。通过一项小规模模拟研究，我们考察了该方法的有限样本性质。