Influence Ranking Based on Tilting with Application to Climate Data

The tilting method ranks each observation in terms of its influence on a general statistic, which can be mean, covariance, etc. This approach is based on ‘tilting’ or re-weighting each data value to achieve a given small change of the statistic, while minimizing the total amount of tilt. Then the influence ranking for each data corresponds to the rank of the tilted data weights. The tilting method can be applied to univariate, multivariate, functional or multivariate functional data. It allows for robust analysis and outlier detection. Climate data are intrinsically functional, either temporally or spatially or both. We illustrate the use of the tilting method by applying it to sea surface temperature data and bivariate data of mean monthly temperatures and precipitations recorded at Canadian weather stations.