Recently, Marengo and Settepanella (2010) introduced a model of social choice among bundles of interdependent elements. In this paper we prove that their voting model is highly decidable, i.e. a group of agents that agrees to use such voting process has an high probability to reach a final...

In this paper we develop on a geometric model of social choice among bundles of interdependent elements (objects). Social choice can be seen as a process of search for optima in a complex multi-dimensional space and objects determine a decomposition of such a space into subspaces. We present a...

We consider goodness-of-fit tests of Cauchy distribution based on weighted integrals of the squared distance of the difference between the empirical characteristic function of the standardized data and the characteristic function of the standard Cauchy distribution. For standardization of data...

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) zi , i =1,...,n, Anderson and Stephens (1972) proposed testing procedures based on the statistics Smax = maxuS (u) and S min = minuS (u), where u is a unit vector and nS (u) is the sum of square...

We propose improvements in numerical evaluation of symmetric stable density and its partial derivatives with respect to the parameters. They are useful for more reliable evaluation of maximum likelihood estimator and its standard error. Numerical values of the Fisher information matrix of...

We propose a test of equality of two covariance matrices based on the maximum standardized di erence of scalar covariances of two sample covariance matrices.We derive the tail probability of the asymptotic null distribution of the test statistic by the tube method.However the usual formal tube...

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 property of a stock price process can be tested based on the capital process of a betting strategy. In particular...

We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is lucidly expressed in terms of the past average of...

We introduce a new formulation of asset trading games in continuous time in the framework of the game-theoretic probability established by Shafer and Vovk (Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation, the market moves continuously, but an investor trades in...

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 Vovk. We also show that, as the number of rounds goes to infinity, the upper hedging price of a European option...