Lambert W random variables - a new family of generalized skewed distributions with applications to risk estimation

Originating from a system theory and an input/output point of view, I introduce a new class of generalized distributions. A parametric nonlinear transformation converts a random variable $X$ into a so-called Lambert $W$ random variable $Y$, which allows a very flexible approach to model skewed data. Its shape depends on the shape of $X$ and a skewness parameter $\gamma$. In particular, for symmetric $X$ and nonzero $\gamma$ the output $Y$ is skewed. Its distribution and density function are particular variants of their input counterparts. Maximum likelihood and method of moments estimators are presented, and simulations show that in the symmetric case additional estimation of $\gamma$ does not affect the quality of other parameter estimates. Applications in finance and biomedicine show the relevance of this class of distributions, which is particularly useful for slightly skewed data. A practical by-result of the Lambert $W$ framework: data can be "unskewed." The $R$ package http://cran.r-project.org/web/packages/LambertWLambertW developed by the author is publicly available (http://cran.r-project.orgCRAN).Comment: Published in at http://dx.doi.org/10.1214/11-AOAS457 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Forecastable Component Analysis (ForeCA)

I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time series into a forecastable and an orthogonal white noise space. I present a converging algorithm with a fast eigenvector solution. Applications to financial and macro-economic time series show that ForeCA can successfully discover informative structure, which can be used for forecasting as well as classification. The R package ForeCA (http://cran.r-project.org/web/packages/ForeCA/index.html) accompanies this work and is publicly available on CRAN.Comment: 10 pages, 4 figures; ICML 201

Presentation Effects in Cross-Cultural Experiments - An Experimental Framework for Comparisons

This paper investigates the impact of game presentation dependent on ethnical affiliation. Two games representing the same logical and strategical problem are introduced. Presented games are continuous prisoner’s dilemma games where decision makers can choose an individual level of cooperation from a given range of possible actions. In the first condition, a positive transfer creates a positive externality for the opposite player. In the second condition, this externality is negative. Accomplishing a cross-cultural experimental study involving subjects from the West Bank and Jerusalem (Israel) we test for a strategic presentation bias applying these two conditions. Subjects in the West Bank show a substantially higher cooperation level in the positive externality treatment. In Jerusalem no presentation effect is observed. Critically discussing our findings, we argue that a cross-cultural comparison leads to only partially meaningful and opposed results if only one treatment condition is evaluated. We therefore suggest a complementary application and consideration of different presentations of identical decision problems within cross-cultural research.Cooperation, presentation of decision problems, framing, methodology, cross-cultural research

Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction

We introduce 'mixed LICORS', an algorithm for learning nonlinear, high-dimensional dynamics from spatio-temporal data, suitable for both prediction and simulation. Mixed LICORS extends the recent LICORS algorithm (Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a non-parametric, EM-like soft clustering. This retains the asymptotic predictive optimality of LICORS, but, as we show in simulations, greatly improves out-of-sample forecasts with limited data. The new method is implemented in the publicly-available R package "LICORS" (http://cran.r-project.org/web/packages/LICORS/).Comment: 11 pages; AISTATS 201

Experimental Investigation of a Cyclic Duopoly Game

The notion of a cyclic game has been introduced by Selten and Wooders (2001). They illustrate the concept by the analysis of a cyclic  duopoly game. The experiments reported concern this game. The game was played by eleven matching groups of six players each. The observed choice fre- quencies were compared with the predictions of Nash equilibrium, impulse balance equilibrium (Selten, Abbink and Cox (2005), Selten and Chmura (2007)) and two-sample equilbrium (Osborne and Rubinstein(1998)). Pair- wise comparisons by the Wilcoxon Signed-rank test show that impulse balance equilibrium as well as two-sample equilibrium have a significantly better predictive success than Nash equilibrium. The difference between impulse balance equilibrium and two-sample equilibrium is not   significant.In each matching group three players acted only in uneven periods and   the other three only in even periods. This game has two pure strategy equi- libria in which both types of players behave differently. The data exhibit a weak but significant tendency in the direction of coordination at a   pure strategy equilibrium.cyclic game duopoly experiment, impulse balance equilibrium, two-sample equilibrium