Abstract

this article, we propose a procedure called Enhanced FDR (EFDR), which is based on controlling the false discovery rate (FDR) and a concept known as generalized degrees of freedom (GDF). EFDR differs from the standard FDR procedure through its reducing of the number of hypotheses tested. This is done in two ways: first, the model is represented more parsimoniously in the wavelet domain, and second, an optimal selection of hypotheses is made using a criterion based on generalized degrees of freedom. Not only does the EFDR procedure tell us whether a spatial signal is present or not, it has an added bonus that, if a signal is deemed present, it can indicate its location and magnitude. We examine EFDR's operating characteristics, and in simulations we show that it outperforms the standard FDR and conventional testing procedures. Finally, the EFDR procedure is applied to an air-temperature data set generated from the Climate System Model (CSM) of the National Center for Atmospheric Research (NCAR), where air temperatures in the 1980s are compared to those in the 1990s. We conclude that temperature change has occurred between the two decades, mostly warming in the central part of the USA and in coastal regions of South America at about 20 S. Key words: Denoising, false discovery rate, generalized degrees of freedom, pixel, power, signal detection, wavelets

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