False Discovery Rates to Detect Signals from Incomplete Spatially Aggregated Data
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There are a number of ways to test for the absence/presence of a spatial signal in a completely observed fine-resolution image. One of these is a powerful nonparametric procedure called EFDR (Enhanced False Discovery Rate). A drawback of EFDR is that it requires the data to be defined on regular pixels in a rectangular spatial domain. Here, we develop an EFDR procedure for possibly incomplete data defined on irregular small areas. We use conditional simulation to condition on the available data and simulate the full rectangular image at its finest resolution many times (M, say). EFDR is applied to each of these simulations resulting in M statistically dependent p-values. We test the original null hypothesis of no signal by combining these p-values using copulas and a composite likelihood. If the null hypothesis of no signal is rejected, we then estimate the spatial signal. A simulation study and an application to temperature change in the Asia-Pacific are given to demonstrate the effectiveness of our proposed procedure.
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