Influence of single observations on the choice of the penalty parameter in ridge regression

Penalized regression methods, such as ridge regression, heavily rely on the choice of a tuning, or penalty, parameter, which is often computed via cross-validation. Discrepancies in the value of the penalty parameter may lead to substantial differences in regression coefficient estimates and predictions. In this paper, we investigate the effect of single observations on the optimal choice of the tuning parameter, showing how the presence of influential points can dramatically change it. We distinguish between points as "expanders" and "shrinkers", based on their effect on the model complexity. Our approach supplies a visual exploratory tool to identify influential points, naturally implementable for high-dimensional data where traditional approaches usually fail. Applications to real data examples, both low- and high-dimensional, and a simulation study are presented.Comment: 26 pages, 6 figure

Yield predictions of timothy (Phleum pratense L.) in Norway under future climate scenarios

The perennial forage grass timothy (Phleum pratense L.) is the most important forage crop in Norway. Future changesin the climate will affect growing conditions and hence the yield output. We used data from the Norwegian Value for Cultivation and Use testing to find a statistical prediction model for total dry matter yield (DMY) based on agro-climatic variables. The statistical model selection found that the predictors with the highest predictive power were growing degree days (GDD) in July and the number of days with rain (>1mm) in June–July. These predictors together explained 43% of the variability in total DMY. Further, the prediction model was combined with a range of climate ensembles (RCP4.5) to project DMY of timothy for the decades 2050–2059 and 2090–2099 at 8 locations in Norway. Our projections forecast that DMY of today’s timothy varieties may decrease substantially in South-Eastern Norway, but increase in Northern Norway, by the middle of the century, due to increased temperatures and changing precipitation patterns

Yield predictions of timothy (Phleum pratense L.) in Norway under future climate scenarios

The perennial forage grass timothy (Phleum pratense L.) is the most important forage crop in Norway. Future changes in the climate will affect growing conditions and hence the yield output. We used data from the Norwegian Value for Cultivation and Use testing to find a statistical prediction model for total dry matter yield (DMY) based on agro-climatic variables. The statistical model selection found that the predictors with the highest predictive power were growing degree days (GDD) in July and the number of days with rain (>1mm) in June–July. These predictors together explained 43% of the variability in total DMY. Further, the prediction model was combined with a range of climate ensembles (RCP4.5) to project DMY of timothy for the decades 2050–2059 and 2090–2099 at 8 locations in Norway. Our projections forecast that DMY of today’s timothy varieties may decrease substantially in South-Eastern Norway, but increase in Northern Norway, by the middle of the century, due to increased temperatures and changing precipitation patterns