Nonparametric Statistical Inference via Metric Distribution Function in Metric Spaces.

ABSTRACT: The distribution function is essential in statistical inference and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces and are no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the concept of the distribution function in a more general space to meet emerging needs. Note that the linearity allows us to use hypercubes to define the distribution function in a Euclidean space. Still, without the linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce

SUBMITTER: Wang X 

PROVIDER: S-EPMC11902916 | biostudies-literature | 2024

REPOSITORIES: biostudies-literature