Unbiased risk estimation and scoring rules

Stein unbiased risk estimation is generalized twice, from the Gaussian shift model to nonparametric families of smooth densities, and from the quadratic risk to more general divergence type distances. The development relies on a connection with local proper scoring rules.Comment: This is the author's version of a work that was accepted for publication in Comptes rendus Mathematiqu

Local proper scoring rules of order two

Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if it encourages truthful reporting. It is local of order $k$ if the score depends on the predictive density only through its value and the values of its derivatives of order up to $k$ at the realizing event. Complementing fundamental recent work by Parry, Dawid and Lauritzen, we characterize the local proper scoring rules of order 2 relative to a broad class of Lebesgue densities on the real line, using a different approach. In a data example, we use local and nonlocal proper scoring rules to assess statistically postprocessed ensemble weather forecasts.Comment: Published in at http://dx.doi.org/10.1214/12-AOS973 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Joint European development strategy

On July 27,1971, the Commission of the European Communities has submitted a memorandum on a Joint European development policy to the governments of the EEC’s member states. It has thereby called for a beginning of the discussion on cooperative action by the Communities also in the field of development policies

Investors care about risk, but can't cope with volatility

Following the classical portfolio theory all an investor has to do for an optimal investment is to determine his risk attitude. This allows him to find his point on the capital market line by combining a risk-free asset with the market portfolio. We investigate the following research questions in an experimental set-up: Do private investors see a relationship between risk attitude and the amount invested risky at all and do they adjust their investments if provided with different risk levels of the risky asset? To answer these questions we ask subjects in a between subject design to allocate a certain amount between a risky and a risk-free asset. Risky assets differ between conditions, but can be transformed into each other by combining them with the risk-free asset. We find that mainly investors risk attitude, but also their risk perception, and the investment horizon are strong predictors for risk taking. Indeed, investors do not appear to be naïve, but they do something sensitive. Nevertheless, we observe a strong framing effect: investors choose almost the same allocation to the risky asset independently of changes in its risk-return profile thus ending up with significantly different volatilities. Feedback does not mitigate the framing effect. The effect is somewhat smaller for investors with a high financial literacy. Overall, people seem to use two mental accounts, one for the risk-free and one for the risky investment with the risk attitude determining the percentage allocation to the risky asset and not the chosen portfolio volatility

Raising awareness for water polution based on game activities using internet of things

Awareness among young people regarding the environment and its resources and comprehension of the various factors that interplay, is key to changing human behaviour towards achieving a sustainable planet. In this paper IoT equipment, utilizing sensors for measuring various parameters of water quality, is used in an educational context targeting at a deeper understanding of the use of natural resources towards the adoption of environmentally friendly behaviours. We here note that the use of water sensors in STEM gameful learning is an area which has not received a lot of attention in the previous years. The IoT water sensing and related scenaria and practices, addressing children via discovery, gamification, and educational activities, are discussed in detail