论文标题
内核平均嵌入概率度量及其在功能数据分析中的应用
Kernel Mean Embedding of Probability Measures and its Applications to Functional Data Analysis
论文作者
论文摘要
这项研究打算在功能响应统计模型引起的无限分离的希尔伯特空间上引入内核平均概率度量的嵌入。嵌入式函数代表了小型开放社区中概率度量的浓度，该邻域识别伪样性，并为统计推断提供了丰富的框架。利用最大平均差异，我们在功能响应模型中设计了新的测试。在功能数据分析的三个主要问题中，对竞争对手进行了新的衍生测试的性能，包括功能 - 刻录回归，功能性单向方差分析和协方差运算符的平等性。
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.
