9 papers
Group invariance of -divergences and the Fisher--Rao distance
Frank Nielsen, Kazuki Okamura
Many statistical models have natural symmetries described by a group action. We study how such symmetries affect the comparison of two distributions. We work with a transformation…
Asymptotic estimates for multiple point ranges of transient random walks on graphs
Kazuki Okamura
We study multiple point ranges for random walks on graphs, extending known asymptotic results obtained for random walks on groups. A distinctive feature is that algebraic and trans…
A remark on the comparison of the sum and the maximum of positive random variables
Kazuki Okamura
We disprove a conjecture stated in a recent paper by Arnold and Villasenor concerning the sum and the maximum of independent and identically distributed half-normal random variable…
Quantitative estimates for singularity for conjugate equations driven by linear fractional transformations
Kazuki Okamura
We consider the conjugate equation driven by two families of finite maps on the unit interval satisfying a compatibility condition. This framework contains de Rham's functional equ…
Asymptotics of the maximum likelihood estimator of the location parameter of Pearson Type VII distribution
Kazuki Okamura
We study the maximum likelihood estimator of the location parameter of the Pearson Type VII distribution with known scale. We rigorously establish precise asymptotic properties suc…
Singularity for graph-directed conjugate equations indexed by a two-vertex digraph
Kazuki Okamura
We study graph-directed conjugate functional equations on the unit interval indexed by the complete digraph with self-loops on two vertices. We focus on the singularity and regular…