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

Temporal modulation transfer functions in the European Starling (Sturnus vulgaris): II. Responses of auditory-nerve fibres

The temporal resolution of cochlear-nerve fibres in the European starling was determined with sinusoidally amplitude-modulated noise stimuli similar to those previously used in a psychoacoustic study in this species (Klump and Okanoya, 1991). Temporal modulation transfer curves (TMTFs) were constructed for cochlear afferents allowing a direct comparison with the starling's behavioural performance. On average, the neuron's detection of modulation was less sensitive than that obtained in the behavioural experiments, although the most sensitive cells approached the values determined psychophysically. The shapes of the neural TMTFs generally resembled low-pass or band-pass filter functions, and the shapes of the averaged neural functions were very similar to those obtained in the behavioural study for two different types of stimuli (gated and continuous carrier). Minimum integration times calculated from the upper cut-off frequency of the neural TMTFs had a median of 0.97 ms with a range of 0.25 to 15.9 ms. The relations between the minimum integration times and the tuning characteristics of the cells (tuning curve bandwidth, Q10 dB-value, high- and low-frequency slopes of the tuning curves) are discussed. Finally, we compare the TMTF data recorded in the starling auditory nerve with data from neurophysiological and behavioural observations on temporal resolution using other experimental paradigms in this and other vertebrate species

Judicial Retirements and the Staying Power of U.S. Supreme Court Decisions

The influence of U.S. Supreme Court majority opinions depends critically on how these opinions are received and treated by lower courts, which decide the vast majority of legal disputes. We argue that the retirement of Justices on the Supreme Court serves as a simple heuristic device for lower court judges in deciding how much deference to show to Supreme Court precedent. Using a unique dataset of the treatment of all Supreme Court majority opinions in the courts of appeals from 1953 to 2012, we find that negative treatments of Supreme Court opinions increase, and positive treatments decrease, as the Justices who supported a decision retire from the Court. Importantly, this effect exists over and above the impact of retirements on the ideological makeup of the Supreme Court

Nonprofit Organizations as Ideal Type of Socially Responsible and Impact Investors

Nonprofit organizations (NPOs) as mission-driven organizations could profit from investing in stocks diametrically opposed to their mission, as they serve as a perfect hedge. Earning more income from oil or tobacco companies when there is a greater need for ecological interventions or cancer research might help effectively fighting the cause. We show the flaw in this logic as in its optimal state, this strategy is at most a financial zero-sum game. However, as NPOs strive at creating net value by aiming at a most effective mission-accomplishment, socially responsible and impact investments may offer a better way of doing so. We present NPOs as an ideal type of a socially responsible and impact investor and give the corresponding formal economic reasoning. For mission-driven organizations only the combination of financial and mission-based goals allows for an effective, goal-oriented financial decision-making. The full application of this logic is what is broadly understood under the term of mission investing (MI). Based on a theoretic introduction, we present a formalized way of analyzing multidimensional tradeoffs in the case of NPOs being mission-driven investors. This formalization will supply NPOs with a tool that enables them to capture their investments’ financial and mission-based impact and therefore the full benefit of responsible and impact-driven investments