Increasing Power When Controlling Multiple Hypothesis Testing with Climate Data via Covariate Smoothing

Abstract Whenever many hypothesis tests are performed simultaneously, the risks of falsely rejecting some null hypotheses must be accounted for in statistical analyses. Methods controlling the possibility of any false rejections become very conservative as the number of tests grows, which motivated the false discovery rate (FDR) control framework that limits the average proportion of rejections that are false. However, FDR control methods, such as Benjamini–Hochberg, often have undesirably low power when working in spatially correlated settings. Here we focus on regression problems in large climate datasets involving a univariate response variable and spatially gridded covariate data. Given that nearby locations are more likely to share a signal, we propose a method in which the covariates are spatially smoothed with locally fitted covariance functions before applying the hypothesis testing procedure. Simulation results show that by using Benjamini–Hochberg with this smoothed data, power is increased while still maintaining empirical FDR control. We then apply the technique to real sea surface temperature covariates with both simulated and real responses. The real data example, linking sea surface temperatures to July temperatures in the central US, demonstrates that the smoothing procedure allows for signals to be identified when none pass traditional Benjamini–Hochberg. The proposed procedure provides climate scientists with a simple yet powerful tool for extracting more information from their data, while correcting for multiple hypothesis testing.Supplementary materials accompanying this paper appear online.