3 citations
5 papers
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…
Conformal geometry of statistical manifold with application to sequential estimation
Masayuki Kumon, Akimichi Takemura, Kei Takeuchi
We present a geometrical method for analyzing sequential estimating procedures. It is based on the design principle of the second-order efficient sequential estimation provided in…
Approximations and asymptotics of upper hedging prices in multinomial models
Ryuichi Nakajima, Masayuki Kumon, Akimichi Takemura +1
We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and…
Sequential optimizing strategy in multi-dimensional bounded forecasting games
Masayuki Kumon, Akimichi Takemura, Kei Takeuchi
We propose a sequential optimizing betting strategy in the multi-dimensional bounded forecasting game in the framework of game-theoretic probability of Shafer and Vovk (2001). By s…
New procedures for testing whether stock price processes are martingales
Kei Takeuchi, Akimichi Takemura, Masayuki Kumon
We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale p…