Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models

Outlier detection algorithms are intimately connected with robust statistics that down‐weight some observations to zero. We define a number of outlier detection algorithms related to the Huber‐skip and least trimmed squares estimators, including the one‐step Huber‐skip estimator and the forward search. Next, we review a recently developed asymptotic theory of these. Finally, we analyse the gauge, the fraction of wrongly detected outliers, for a number of outlier detection algorithms and establish an asymptotic normal and a Poisson theory for the gauge.     

Young Norwegians and their views on climate change and the future: findings from a climate concerned and oil-rich nation

Young people represent the future, but little is known about their attitudes towards climate change, one of the most serious issues facing the world today. The purpose of the present study is to contribute with improved and new knowledge of young Norwegians’ understanding of and attitudes towards this issue, with a special focus on perspectives of the future. Of particular interest is the influence of divergent framings of the climate question in Norway, due to conflicting interests between the petroleum industry and climate concern. The young people's voices are elicited through two different surveys undertaken during the fall of 2013, one national (Norwegian Citizen Panel) and one local (School survey conducted among high-school students). The study generated both quantitative and qualitative findings, stemming from closed-ended as well as open-ended questions. The data were handled through a mixed methods approach, combining quantitative and qualitative analyses. The results show that the voices tend to be oriented towards the opinion that Norway has a responsibility to help poor countries as well as a duty to prevent climate change and that the country should reduce its oil production. We further observe that young Norwegians have an optimistic view of the future, based on a pronounced belief in technology and science.     

QMRA for Drinking Water: 2. The Effect of Pathogen Clustering in Single‐Hit Dose‐Response Models

Spatial and/or temporal clustering of pathogens will invalidate the commonly used assumption of Poisson‐distributed pathogen counts (doses) in quantitative microbial risk assessment. In this work, the theoretically predicted effect of spatial clustering in conventional “single‐hit” dose‐response models is investigated by employing the stuttering Poisson distribution, a very general family of count distributions that naturally models pathogen clustering and contains the Poisson and negative binomial distributions as special cases. The analysis is facilitated by formulating the dose‐response models in terms of probability generating functions. It is shown formally that the theoretical single‐hit risk obtained with a stuttering Poisson distribution is lower than that obtained with a Poisson distribution, assuming identical mean doses. A similar result holds for mixed Poisson distributions. Numerical examples indicate that the theoretical single‐hit risk is fairly insensitive to moderate clustering, though the effect tends to be more pronounced for low mean doses. Furthermore, using Jensen's inequality, an upper bound on risk is derived that tends to better approximate the exact theoretical single‐hit risk for highly overdispersed dose distributions. The bound holds with any dose distribution (characterized by its mean and zero inflation index) and any conditional dose‐response model that is concave in the dose variable. Its application is exemplified with published data from Norovirus feeding trials, for which some of the administered doses were prepared from an inoculum of aggregated viruses. The potential implications of clustering for dose‐response assessment as well as practical risk characterization are discussed.     

Does Education Improve Cognitive Performance Four Decades After School Completion?

We study the effect of secondary education on cognitive performance toward the end of working age. We exploit the exogenous variation in years of schooling arising from compulsory schooling reforms implemented in six European countries during the 1950s and 1960s. Using data of individuals, approximately age 60, from the Survey of Health, Ageing and Retirement in Europe (SHARE), we assess the causal effect of education on memory, fluency, numeracy, and orientation-to-date. Furthermore, we study education effects on cognitive decline. We find a positive impact of schooling on memory scores. One year of education increases the memory score approximately four decades later by about 0.2, which amounts to 10 % of a standard deviation. Furthermore, we find some evidence for a protective effect of schooling on cognitive decline in terms of verbal fluency.     

Asymptotic Inference on Cointegrating Rank in Partial Systems

The likelihood ratio test for cointegrating rank is analyzed for partial (or conditional) systems in the vector autoregressive error-correction model. Under the assumption of weak exogeneity for the cointegrating parameters, the asymptotic distributions are given and tables of critical values are provided. A discussion is given of some of the assumptions of the model, why they are needed, and how they are tested.