A unified approach to hypothesis testing is developed for scalar-on-function, function-on-function, function-on-scalar models and particularly mixed models that contain both functional and scalar predictors. In contrast with most existing methods that rest on the large-sample distributions of test statistics, the proposed method leverages the technique of bootstrapping max statistics and exploits the variance decay property that is an inherent feature of functional data, to improve the empirical power of tests especially when the sample size is limited or the signal is relatively weak. Theoretical guarantees on the validity and consistency of the proposed test are provided uniformly for a class of test statistics.
翻译:本文提出了一种统一的假设检验方法,适用于标量对函数、函数对函数、函数对标量的模型以及特别包含函数和标量预测变量的混合模型。与大多数现有的方法依赖于检验统计量的大样本分布不同,所提出的方法利用最大统计量的自助法和函数数据固有的方差衰减特性,从而提高了测试的实证功率,特别是当样本量有限或信号相对较弱时。为一类检验统计量提供了统一的理论保证,证明了所提出测试的有效性和一致性。