  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.
