False discovery rate for functional data

Since Benjamini and Hochberg introduced false discovery rate (FDR) in their seminal paper, this has become a very popular approach to the multiple comparisons problem. An increasingly topic within functional data analysis is local inference, i.e. continuous statistical testing of null hypothesis along domain. The principal issue infinite amount tested hypotheses, which can be seen as an extreme case In we define discuss notion FDR general setting. Moreover, version Benjamini–Hochberg procedure with definition adjusted p value function. Some conditions are stated, under provides control FDR. Two different simulation studies presented; first study one-dimensional domain comparison another state-of-the-art method, second planar two-dimensional Finally, proposed method applied satellite measurements Earth temperature. detail, aim at identifying regions planet where temperature significantly increased last decades. After adjustment, large areas still significant.