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

On the Prevalence of Framing Effects Across Subject-Pools in a Two- Person Cooperation Game

In this experimental study, involving subjects from Abu-Dis (West Bank), Chengdu (China), Helsinki (Finland), and Jerusalem (Israel), we test for a presentation bias in a two-person cooperation game. In the positive frame of the game, a transfer creates a positive externality for the opposite player, and in the negative frame, a negative one. Subjects in Abu-Dis and Chengdu show a substantially higher cooperation level in the positive externality treatment. In Helsinki and Jerusalem, no framing effect is observed. These findings are also reflected in associated first-order beliefs. We argue that comparisons across subject-pools might lead to only partially meaningful and opposed conclusions 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 on subject-pool differences.framing of decision problems, methodology, subject-pool differences