21 citations · 40 across the 16 of their papers we have counts for
16 papers
Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables
Tamio Koyama, Akimichi Takemura
We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function…
A game-theoretic proof of Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair-coin tossing
Takeyuki Sasai, Kenshi Miyabe, Akimichi Takemura
We give a game-theoretic proof of the celebrated Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for fair coin tossing. Our proof, based on Bayesian strategy, is ex…
Conformal Geometry of Sequential Test in Multidimensional Curved Exponential Family
Masayuki Kumon, Akimichi Takemura, Kei Takeuchi
This article presents a differential geometrical method for analyzing sequential test procedures. It is based on the primal result on the conformal geometry of statistical manifold…
Properties of powers of functions satisfying second-order linear differential equations with applications to statistics
Naoki Marumo, Toshinori Oaku, Akimichi Takemura
We derive properties of powers of a function satisfying a second-order linear differential equation. In particular we prove that the n-th power of the function satisfies an (n+1)-t…
Estimation of exponential-polynomial distribution by holonomic gradient descent
Jumpei Hayakawa, Akimichi Takemura
We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random…
The law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges
Kenshi Miyabe, Akimichi Takemura
We prove both the validity and the sharpness of the law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges.