Path connectedness on a space of probability density functions

Abstract

We introduce a class of paths or one-parameter models connecting arbitrary two probability density functions (pdf’s). The class is derived by employing the Kolmogorov-Nagumo average between the two pdf’s. There is a variety of such path connectedness on the space of pdf’s since the Kolmogorov-Nagumo average is applicable for any convex and strictly increasing function. The information geometric insight is provided for understanding probabilistic properties for statistical methods associated with the path connectedness. The one-parameter model is extended to a multidimensional model, on which the statistical inference is characterized by sufficient statistics.