This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of probability measures in small open neighborhoods, which identifies a pseudo-likelihood and fosters a rich framework for statistical inference. Utilizing Maximum Mean Discrepancy, we devise new tests in functional response models. The performance of new derived tests is evaluated against competitors in three major problems in functional data analysis including Function-on-Scalar regression, functional one-way ANOVA, and equality of covariance operators.

中文翻译：

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概率测度的核均值嵌入及其在函数数据分析中的应用

本研究旨在引入由函数响应统计模型引起的无限维可分离希尔伯特空间上的概率度量的核均值嵌入。嵌入函数表示概率度量在小型开放邻域中的集中，它识别伪似然性并培育丰富的统计推断框架。利用最大平均差异，我们设计了功能响应模型的新测试。新派生测试的性能在函数数据分析的三个主要问题上与竞争对手进行评估，包括标量函数回归、函数单向方差分析和协方差算子相等。